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-**/.DS_STORE
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+**/.DS_STORE
+.idea
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+<details>
+<summary>Instructions - click to expand</summary>
+
+- Fork the rfcs repo: https://github.com/pytorch/rfcs
+- Copy `RFC-0000-template.md` to `RFC-00xx-my-feature.md`, or write your own open-ended proposal. Put care into the details.
+- Submit a pull request titled `RFC-00xx-my-feature`.
+    - Assign the `draft` label while composing the RFC. You may find it easier to use a WYSIWYG editor (like Google Docs) when working with a few close collaborators; feel free to use whatever platform you like. Ideally this document is publicly visible and is linked to from the PR.
+    - When opening the RFC for general discussion, copy your document into the `RFC-00xx-my-feature.md` file on the PR and assign the `commenting` label.
+- Build consensus for your proposal, integrate feedback and revise it as needed, and summarize the outcome of the discussion via a [resolution template](https://github.com/pytorch/rfcs/blob/rfc-process/RFC-0000-template.md#resolution).
+    - If the RFC is idle here (no activity for 2 weeks), assign the label `stalled` to the PR.
+- Once the discussion has settled, assign a new label based on the level of support:
+    - `accepted` if a decision has been made in the RFC
+    - `draft` if the author needs to rework the RFC’s proposal
+    - `shelved` if there are no plans to move ahead with the current RFC’s proposal. We want neither to think about evaluating the proposal
+      nor about implementing the described feature until some time in the future.
+- A state of `accepted` means that the core team has agreed in principle to the proposal, and it is ready for implementation.
+- The author (or any interested developer) should next open a tracking issue on Github corresponding to the RFC.
+    - This tracking issue should contain the implementation next steps. Link to this tracking issue on the RFC (in the Resolution > Next Steps section)
+- Once all relevant PRs are merged, the RFC’s status label can be finally updated to `closed`.
+
+</details>
+
+# Special Functions
+
+_Author’s note—This RFC is a work-in-progress._
+
+## Authors
+
+* Allen Goodman (@0x00b1)
+
+## Summary
+
+This proposal concerns adding new operators to PyTorch's special functions module (i.e., `torch.special`). The proposed operators have a wide range of use in scientific computing and numerical methods.
+
+This RFC proposes:
+
+* a coherent philosophy for PyTorch’s special functions module ([torch.special](https://pytorch.org/docs/stable/special.html)) that clearly distinguishes PyTorch’s elementary from special functions; and
+* a set of new [torch](https://pytorch.org/docs/stable/torch.html) and [torch.special](https://pytorch.org/docs/stable/special.html) operators that provide a robust numerical foundation for PyTorch and adhere to the aforementioned philosophy.
+
+This feature has two audiences:
+
+PyTorch users:
+
+* solves the variety of common scientific and engineering problems that special functions address.
+
+PyTorch maintainers:
+
+* provides much needed standardization to committing future operators to PyTorch.
+* provides an extremely useful set of operators that can and should be used for tricky numerical problems (e.g., implementing challenging distribution functions and gradients) and useful decomposition targets.
+
+## Table of Contents
+      
+## Motivation
+
+### What’s a special function?
+
+There’s no formal definition of a “special function.” Colloquially, and for the purpose of this RFC, a special function is a mathematical function that has an established name and notation due to its importance and ubiquity.
+
+## Special Function Policies
+
+PyTorch’s mathematical operators should be categorized as either “elementary” or “special.” An elementary function is a mathematical function whose corresponding operator is available from the `torch` module. A special function is a mathematical function whose corresponding operator is available from the `torch.special` module. Regardless of whether an operator implements an elementary or special function, each operator must share the following properties:
+
+* A name that adheres to the naming policy.
+* A docstring that clearly communicates the following:
+  * A primary definition
+  * Real and complex domains
+  * Real and complex graphs
+* If differentiable, derivtatives for each variable.
+
+### Elementary Functions
+
+Unlike “special functions,”  “elementary functions” have a rigorous definition but, for simplicity, PyTorch uses a simplified definition, categorizing a function as an elementary function if the function is a mathematical function of a single variable (i.e., a unary operator) and the function is one of the following functions or belongs to the following families of functions:
+
+* Cardinal Functions
+* Dirac delta
+* Euler Number
+* Exponential
+* Fibonaci Number
+* Greatest common divisor
+* Hyperbolic
+* Inverse Hyperbolic
+* Inverse Trigonometric
+* Kronecker delta
+* Least common multiple
+* Logarithmic
+* Partitions
+* Power
+* Rounding and Congruence Functions
+* Tensorial Functions
+* Trigonometric
+
+## Proposed Implementation
+
+### Factorials
+
+#### Factorial
+
+```Python
+factorial(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ factorial, if $n \in \mathbb{N}$:
+
+$$n! = \prod_{k = 1}^{n}k.$$
+
+Otherwise:
+
+$$n! = \Gamma(n + 1),$$
+
+where $\Gamma$ is the gamma function.
+
+$n!$ is defined for $\left\\{n \in \mathbb{R} \mid n \geq 0 \vee n \notin \mathbb{Z} \right\\}$ and $\left\\{n \in \mathbb{C} \mid \operatorname{Re}(n) \geq 0 \vee n \notin \mathbb{Z} \right\\}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Natural Logarithm of Factorial
+
+```Python
+ln_factorial(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Natural logarithm of $n^{\text{th}}$ factorial, $\ln{(n!)}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Double Factorial
+
+```Python
+double_factorial(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ double factorial, if $n \in \mathbb{N}$:
+
+$$n!!=\prod_{k = 0}^{\left\lceil\tfrac{n}{2}\right\rceil-1}(n-2k).$$
+
+Otherwise:
+
+$$n!!=\left(\frac{2}{\pi}\right)^{\frac{1}{4}(1-\cos(\pi n))}2^{\tfrac{2}{n}}\Gamma\left(\frac{n}{2}+1\right),$$
+
+where $\Gamma$ is the gamma function.
+
+$n!!$ is defined for $\left\\{n \in \mathbb{R} \mid n \geq 0 \vee \tfrac{n}{2} \notin \mathbb{Z} \right\\}$ and $\left\\{n \in \mathbb{C} \mid n \geq 0 \vee \tfrac{n}{2} \notin \mathbb{Z} \right\\}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Natural Logarithm of Double Factorial
+
+```Python
+ln_double_factorial(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Natural logarithm of $n^{\text{th}}$ double factorial, $\ln{(n!!)}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Rising Factorial
+
+```Python
+rising_factorial(
+    z: Tensor, 
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Rising factorial:
+
+$$z^{n}=\frac{\Gamma(z + n)}{\Gamma(z)},$$
+
+where $\Gamma$ is the gamma function.
+
+$z^{n}$ is defined for all real and complex $z$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $n$ is a number, $z$ must be a tensor.
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – exponent. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Natural Logarithm of Rising Factorial
+
+```Python
+ln_rising_factorial(
+    z: Tensor, 
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Natural logarithm of rising factorial, $\operatorname{ln}{(z^{n})}$.
+
+$\operatorname{ln}{(z^{n})}$ is defined for all real and complex $z$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $n$ is a number, $z$ must be a tensor.
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – exponent. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Falling Factorial
+
+```Python
+falling_factorial(
+    z: Tensor, 
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Falling factorial:
+
+$$z_{n}=\frac{\Gamma(z + 1)}{\Gamma(z - n + 1)},$$
+
+where $\Gamma$ is the gamma function.
+
+$z_{n}$ is defined for all real and complex $z$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $n$ is a number, $z$ must be a tensor.
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – exponent. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Natural Logarithm of Falling Factorial
+
+```Python
+ln_falling_factorial(
+    z: Tensor, 
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Natural logarithm of falling factorial, $\operatorname{ln}{(z_{n})}$.
+
+$\operatorname{ln}{(z_{n})}$ is defined for all real and complex $z$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $n$ is a number, $z$ must be a tensor.
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – exponent. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Combinatorial Numbers and Functions
+
+#### Binomial Coefficient
+
+```Python
+binomial_coefficient(
+    n: Tensor,
+    k: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Binomial coefficient:
+
+$${\binom{n}{k}} = {\frac{n!}{k!(n - k)!}}.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $k$ is a number, $n$ must be a tensor.
+
+**k** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – exponent. If $n$ is a number, $k$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Natural Logarithm of Binomial Coefficient
+
+```Python
+ln_binomial_coefficient(
+    n: Tensor,
+    k: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Natural logarithm of binomial coefficient, $\operatorname{ln}{{\binom{n}{k}}}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $k$ is a number, $n$ must be a tensor.
+
+**k** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – exponent. If $n$ is a number, $k$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Catalan Number
+
+```Python
+catalan_number_c(
+    n: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ Catalan number:
+
+$$C_{z} = \frac{2^{2z}\Gamma(z + \tfrac{1}{2})}{\sqrt{\pi} \Gamma(z + 2)}.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Stirling Number of the First Kind
+
+```Python
+stirling_number_s_1(
+    n: Tensor,
+    m: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Stirling number of the first kind:
+
+$$s(n, k) = $$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Stirling Number of the Second Kind
+
+```Python
+stirling_number_s_2(
+    n: Tensor,
+    m: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Stirling number of the second kind:
+
+$$S(n, k) = {\frac{1}{k!}}\sum_{i = 0}^{k}(-1)^{i}{\binom{k}{i}}(k - i)^{n}.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Bell Number
+
+```Python
+bell_number_b(
+    n: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ Bell number:
+
+$$B_{n}=\sum_{k = 0}^{n}S(n, k).$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Delannoy Number
+
+```Python
+delannoy_number_d(
+    m: Tensor,
+    n: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Delannoy number:
+
+$$D(m, n) = \sum_{k = 0}^{\min(m, n)}\binom{m + n - k}{m}\binom{m}{k}.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Motzkin Number
+
+```Python
+motzkin_number_m(
+    n: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ Motzkin number:
+
+$$M_{n} = \sum_{k = 0}^{\lfloor \frac{n}{2} \rfloor}{\binom{n}{2k}}C_{k}.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Narayana Number
+
+```Python
+narayana_number_n(
+    n: Tensor,
+    k: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Narayana number:
+
+$$N(n, k) = {\frac{1}{n}}\binom{n}{k}\binom{n}{k - 1}.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Schröder Number
+
+```Python
+schroder_number_r(
+    n: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ Schröder number:
+
+$$r_{n} = D(n, n) - D(n + 1, n - 1).$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Gamma and Related Functions
+
+#### Gamma Function
+
+```Python
+gamma(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Gamma function:
+
+$$\Gamma(z)=\int_{0}^{\infty}t^{z-1}e^{-t}dt.$$
+
+$\Gamma(z)$ is defined for $\left\\{n \in \mathbb{R} \mid n > 0 \vee n \notin \mathbb{Z} \right\\}$ and $\left\\{n \in \mathbb{C} \mid \operatorname{Re}(n) > 0 \vee n \notin \mathbb{Z} \right\\}$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Reciprocal Gamma Function
+
+```Python
+reciprocal_gamma(
+    z: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Polygamma Function
+
+```Python
+polygamma(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – derivative.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Digamma Function
+
+```Python
+digamma(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Digamma function:
+
+$$\psi(z)=\sum_{k=1}^{\infty}\left(\frac{1}{k}-\frac{1}{k+z-1}\right)-\gamma.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Trigamma Function
+
+```Python
+trigamma(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Natural Logarithm of the Gamma Function
+
+```Python
+ln_gamma(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Sign of the Gamma Function
+
+```Python
+sign_gamma(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Beta Function
+
+```Python
+beta(
+    a: Tensor, 
+    b: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Beta function:
+
+$$\operatorname{B}(a, b) = \frac{\Gamma(a) \Gamma(b)}{\Gamma(a + b)}$$
+
+where $\Gamma$ is the gamma function.
+
+##### Parameters
+
+**a** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) –
+
+**b** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Natural Logarithm of the Beta Function
+
+```Python
+ln_beta(
+    a: Tensor, 
+    b: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**a** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) –
+
+**b** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Exponential and Logarithmic Integrals
+
+#### Exponential Integral, $\operatorname{Ein}$
+
+```Python
+exponential_integral_ein(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Exponential integral:
+
+$$\operatorname{Ein}(z)=\int_{0}^{z}(1-e^{-t}){\frac{dt}{t}}.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Exponential Integral, $\operatorname{Ei}$
+
+```Python
+exponential_integral_ei(
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Exponential integral:
+
+$$\operatorname{Ei}(z) = \sum_{k = 1}^{\infty} \frac{z^{k}}{k k!} + \gamma + \frac{1}{2}(\ln{(z)} - \ln{(\tfrac{1}{z})}).$$
+
+##### Parameters
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Exponential Integral, $E_{1}$
+
+```Python
+exponential_integral_e_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Exponential integral:
+
+$$E_{1}(z)=\int _{z}^{\infty}{\frac{e^{-t}}{t}}.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Exponential Integral, $E_{n}$
+
+```Python
+exponential_integral_e(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Exponential integral:
+
+$$E_{n}(x)=\int_{1}^{\infty}{\frac{e^{-xt}}{t^{n}}}dt.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Logarithmic Integral
+
+```Python
+logarithmic_integral_li(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Logarithmic integral:
+
+$$\operatorname{li}(z)=\int_{0}^{z}{\frac{1}{\ln{(t)}}}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Error and Related Functions
+
+#### Error Function
+
+```Python
+error_erf(z: Tensor, *, out: Optional[Tensor] = None) -> Tensor
+```
+
+Error function: 
+
+$$\operatorname{erf}(z) = \frac{2}{\sqrt{\pi}} \sum_{k = 0}^{\infty } \frac{-1^{k} z^{2k + 1}}{k!(2k + 1)}.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Complementary Error Function
+
+```Python
+error_erfc(z: Tensor, *, out: Optional[Tensor] = None) -> Tensor
+```
+
+Complementary error function:
+
+$$\operatorname{erfc}(z) = 1 - \frac{2}{\sqrt{\pi}} \sum_{k = 0}^{\infty} \frac{-1^{k} z^{2k + 1}}{k!(2k + 1)}.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Imaginary Error Function
+
+```Python
+error_erfi(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Imaginary error function:
+
+$$\operatorname{erfc}(z) = \frac{2}{\sqrt{\pi}} \sum_{k = 0}^{\infty} \frac{z^{2k + 1}}{k!(2k + 1)}.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Inverse Error Function
+
+```Python
+error_inverse_erf(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Inverse error function:
+
+$$\operatorname{erf}^{-1}(z)=\sum_{k=0}^{\infty}{\frac{c_{k}}{2k+1}}({\frac{\sqrt{\pi}}{2}}z)^{2k+1}$$
+
+where $c_{0}=1$ and:
+
+$$c_{k}=\sum_{m=0}^{k-1}{\frac{c_{m}c_{k-1-m}}{(m+1)(2m+1)}}.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Inverse Complementary Error Function
+
+```Python
+error_inverse_erfc(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Dawson and Fresnel Integrals
+
+#### Dawson’s Integral
+
+```Python
+dawson_integral_f(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Dawson’s integral:
+
+$$\operatorname{F}(z)=e^{-z^{2}}\int_{0}^{z}e^{t^{2}}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Sine Fresnel Integral
+
+```Python
+fresnel_integral_s(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Fresnel integral:
+
+$$\operatorname{S}(z)=\int_{0}^{x}\sin{t^{2}}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Cosine Fresnel Integral
+
+```Python
+fresnel_integral_c(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Fresnel integral:
+
+$$\operatorname{C}(z)=\int_{0}^{x}\cos{t^{2}}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Trigonometric and Hyperbolic Integrals
+
+#### Sine Integral ($operatorname{Sin}$)
+
+```Python
+sine_integral_sin(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Sine integral:
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Sine Integral ($\operatorname{Si}$)
+
+$$\operatorname{Sin}(z)=\int_{0}^{z}{\frac{\sin{t}}{t}}dt.$$
+
+```Python
+sine_integral_si(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Sine integral:
+
+$$\operatorname{Si}(z)=-\int_{z}^{\infty }{\frac{\sin{t}}{t}}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Cosine Integral ($\operatorname{Cin}$)
+
+```Python
+cosine_integral_cin(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Cosine integral:
+
+$$\operatorname{Cin}(z)=\int_{0}^{z}{\frac{1-\cos{t}}{t}}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Cosine Integral ($\operatorname{Ci}$)
+
+```Python
+cosine_integral_ci(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Cosine integral:
+
+$$\operatorname{Ci}(z)=\gamma+\ln{z}-\int_{0}^{z}{\frac{1-\cos{t}}{t}}$$
+
+where $\gamma$ is the Euler–Mascheroni constant.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Hyperbolic Sine Integral
+
+```Python
+hyperbolic_sine_integral_shi(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Hyperbolic sine integral:
+
+$$\operatorname{Shi}(z)=\int_{0}^{z}{\frac{\sinh{t}}{t}}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Hyperbolic Cosine Integral
+
+```Python
+hyperbolic_cosine_integral_chi(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Hyperbolic cosine integral:
+
+$$\operatorname{Chi}(z)=\gamma+\ln{z}+\int_{0}^{z}{\frac{\cosh{t-1}}{t}}dt.$$
+
+where $\gamma$ is the Euler–Mascheroni constant.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Incomplete Gamma and Related Functions
+
+#### Incomplete Gamma Function ($\gamma$)
+
+```Python
+lower_incomplete_gamma(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Lower incomplete gamma function:
+
+$$\Gamma(s,z)=\int_{z}^{\infty}t^{s-1}e^{-t}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Incomplete Gamma Function ($\Gamma$)
+
+```Python
+upper_incomplete_gamma(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Upper incomplete gamma function:
+
+$$\gamma(s,z)=\int_{0}^{z}t^{s-1}e^{-t}dt.$$
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Incomplete Beta Function
+
+```Python
+incomplete_beta(
+    z: Tensor, 
+    a: Tensor, 
+    b: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+**a** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**b** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Airy Functions
+
+Functions defined as the two, linearly independent solutions to:
+
+$$y'' - yz = 0.$$
+
+#### Airy Function of the First Kind
+
+```Python
+airy_ai(
+    z: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Airy function of the first kind:
+
+$$\operatorname{Ai}(z)={\frac{1}{3^{\tfrac{2}{3}}\Gamma(\tfrac{2}{3})}} {_0F_1(; \tfrac{2}{3}; \tfrac{1}{9}; z^{3})} - \frac{z}{3^{\tfrac{1}{3}}\Gamma(\tfrac{1}{3})} {_0F_1(; \tfrac{4}{3}; \tfrac{1}{9}; z^{3})}$$
+
+where $\Gamma$ is the gamma function and $_0F_1(; a; z)$ is the confluent hypergeometric limit function.
+
+$\operatorname{Ai}(z)$ is defined for all real and complex values.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Airy Function of the Second Kind
+
+```Python
+airy_bi(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Airy function of the second kind:
+
+$$\operatorname{Bi}(z)=\frac{_0F_1\left(;\frac{2}{3};\frac{z^3}{9}\right)}{\sqrt[6]{3} \Gamma \left(\frac{2}{3}\right)}+\frac{\sqrt[6]{3} z _0F_1\left(;\frac{4}{3};\frac{z^3}{9}\right)}{\Gamma \left(\frac{1}{3}\right)}$$
+
+where $\Gamma$ is the gamma function and $_0F_1(; a; z)$ is the confluent hypergeometric limit function.
+
+$\operatorname{Bi}(z)$ is defined for all real and complex values.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Derivative of the Airy Function of the First Kind
+
+```Python
+airy_ai_derivative(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Derivative of the Airy function of the first kind:
+
+$$\operatorname{Ai}'(z)=\frac{z^2 \\,_0F_1\left(;\frac{5}{3};\frac{z^3}{9}\right)}{2\ 3^{\tfrac{2}{3}} \Gamma \left(\frac{2}{3}\right)}-\frac{\\, _0F_1\left(;\frac{1}{3};\frac{z^3}{9}\right)}{\sqrt[3]{3} \Gamma \left(\frac{1}{3}\right)},$$
+
+where $\Gamma$ is the gamma function and $_0F_1(; a; z)$ is the confluent hypergeometric limit function.
+
+$\operatorname{Ai}'(z)$ is defined for all real and complex values.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Derivative of the Airy Function of the Second Kind
+
+```Python
+airy_bi_derivative(
+    z: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Derivative of the Airy function of the second kind:
+
+$$\operatorname{Bi}'(z)=\frac{z^2 \\, _0F_1\left(;\frac{5}{3};\frac{z^3}{9}\right)}{2 \sqrt[6]{3} \\, \Gamma \left(\frac{2}{3}\right)}+\frac{\sqrt[6]{3} \\, _0F_1\left(;\frac{1}{3};\frac{z^3}{9}\right)}{\Gamma \left(\frac{1}{3}\right)},$$
+
+where $\Gamma$ is the gamma function and $_0F_1(; a; z)$ is the confluent hypergeometric limit function.
+
+$\operatorname{Bi}'(z)$ is defined for all real and complex values.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Exponentially Scaled Airy Function of the First Kind
+
+```Python
+exp_airy_ai(
+    z: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Exponentially scaled Airy function of the first kind, $\operatorname{exp}(\operatorname{Ai}(z))$.
+
+$\exp{(\operatorname{Ai}(z))}$ is defined for all real and complex values.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Exponentially Scaled Airy Function of the Second Kind
+
+```Python
+exp_airy_bi(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Exponentially scaled Airy function of the second kind, $\operatorname{exp}(\operatorname{Bi}(z))$.
+
+$\exp{(\operatorname{Bi}(z))}$ is defined for all real and complex values.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Exponentially Scaled Derivative of the Airy Function of the First Kind
+
+```Python
+exp_airy_ai_derivative(
+    z: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Exponentially scaled Derivative of the Airy function of the first kind, $\operatorname{exp}(\operatorname{Ai'}(z))$.
+
+$\exp{(\operatorname{Ai}'(z))}$ is defined for all real and complex values.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Exponentially Scaled Derivative of the Airy Function of the Second Kind
+
+```Python
+exp_airy_bi_derivative(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Exponentially scaled Derivative of the Airy function of the second kind, $\operatorname{exp}(\operatorname{Bi'}(z))$.
+
+$\exp{(\operatorname{Bi}'(z))}$ is defined for all real and complex values.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Bessel Functions
+
+#### Bessel Function of the First Kind
+
+```Python
+bessel_j(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Bessel function of the first kind:
+
+$$J_{n}(z)=\sum _{k=0}^{\infty } \frac{(-1)^k \left(\frac{z}{2}\right)^{2k+n}}{\Gamma (k+\nu +1) k!},$$
+
+where $\Gamma$ is the gamma function.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $n$ is a number, $z$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Bessel Function of the First Kind of Order 0
+
+```Python
+bessel_j_0(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Bessel function of the first kind of order $0$, $J_{0}(z)$
+
+$J_{0}(z)$ is defined for all real and complex $z$.
+
+#### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Bessel Function of the First Kind of Order 1
+
+```Python
+bessel_j_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Bessel function of the first kind of order $1$, $J_{1}(z)$
+
+$J_{1}(z)$ is defined for all real and complex $z$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Bessel Function of the Second Kind
+
+```Python
+bessel_y(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Bessel function of the second kind, if, and only if $\nu \notin \mathbb{Z}$:
+
+$$Y_{\nu }(z)=\csc (\pi  \nu ) (\cos (\nu  \pi ) J_{\nu }(z)-J_{-\nu }(z)),$$
+
+where $J_{n}(z)$ is the Bessel function of the first kind.
+
+If $z \in \mathbb{R}$, $Y_{n}(z)$ is defined for $z > 0$. 
+
+If $z \in \mathbb{C}$, $Y_{n}(z)$ is defined for $z \neq 0$. 
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $n$ is a number, $z$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Bessel Function of the Second Kind of Order 0
+
+```Python
+bessel_y_0(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Bessel function of the second kind of order $0$, $Y_{0}(z)$.
+
+$Y_{0}(z)$ is defined for $\\{z \in \mathbb{R}\\}$ and $\\{z \in \mathbb{C} \mid z \neq 0\\}$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Bessel Function of the Second Kind of Order 1
+
+```Python
+bessel_y_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Bessel function of the second kind of order $1$, $Y_{1}(z)$.
+
+$Y_{1}(z)$ is defined for $\\{z \in \mathbb{R} \mid z > 0\\}$ and $\\{z \in \mathbb{C} \mid z \neq 0\\}$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Hankel Functions
+
+#### Hankel Function of the First Kind
+
+```Python
+hankel_h_1(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Hankel function of the first kind:
+
+$$H_{n}^{1}(z) = J_{n}(z) + i Y_{n}(z),$$
+
+where $J_{n}(z)$ is the Bessel function of the first kind, $i$ is the imaginary unit, and $Y_{n}(z)$ is the Bessel function of the second kind.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Hankel Function of the Second Kind
+
+```Python
+hankel_h_2(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Hankel function of the second kind:
+
+$$H_{n}^{2}(z) = J_{n}(z) - i Y_{n}(z),$$
+
+where $J_{n}(z)$ is the Bessel function of the first kind, $i$ is the imaginary unit, and $Y_{n}(z)$ is the Bessel function of the second kind.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Modified Bessel Functions
+
+#### Modified Bessel Function of the First Kind
+
+```Python
+modified_bessel_i(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Modified Bessel function of the first kind:
+
+$$I_{\nu }(z)=\sum _{k=0}^{\infty } \frac{\left(\frac{z}{2}\right)^{2 k+\nu }}{\Gamma (k+\nu +1) k!}.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Bessel Function of the First Kind of Order 0
+
+```Python
+modified_bessel_i_0(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Modified Bessel function of the first kind of order $0$, $I_{0}(z)$.
+
+$I_{0}(z)$ is defined for all real and complex $z$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Bessel Function of the First Kind of Order 1
+
+```Python
+modified_bessel_i_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Modified Bessel function of the first kind of order $1$, $I_{1}(z)$.
+
+$I_{1}(z)$ is defined for all real and complex $z$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Bessel Function of the Second Kind
+
+```Python
+modified_bessel_k(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Modified Bessel function of the second kind:
+
+$$K_{n}(z) = \frac{1}{2} \pi i^{n + 1} H_n^{1}(i z),$$
+
+where $i$ is the imaginary unit and $H_{n}^{1}(z)$ is the Hankel function of the first kind.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Bessel Function of the Second Kind of Order 0
+
+```Python
+modified_bessel_k_0(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Modified Bessel function of the first kind of order $0$, $K_{0}(z)$.
+
+$K_{0}(z)$ is defined for $\\{z \in \mathbb{R} \mid z > 0\\}$ and $\\{z \in \mathbb{C} \mid z \neq 0\\}$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Bessel Function of the Second Kind of Order 1
+
+```Python
+modified_bessel_k_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Modified Bessel function of the first kind of order $1$, $K_{1}(z)$.
+
+$K_{1}(z)$ is defined for $\\{z \in \mathbb{R} \mid z > 0\\}$ and $\\{z \in \mathbb{C} \mid z \neq 0\\}$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Spherical Bessel Functions
+
+#### Spherical Bessel Function of the First Kind
+
+```Python
+spherical_bessel_j(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Spherical Bessel function of the first kind:
+
+$$j_{n}(x)={\sqrt{\frac{\pi}{2x}}}J_{n + {\frac{1}{2}}}(x).$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Spherical Bessel Function of the First Kind of Order 0
+
+```Python
+spherical_bessel_j_0(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Spherical Bessel function of the first kind:
+
+$$j_{n}(x)={\sqrt{\frac{\pi}{2x}}}J_{n + {\frac{1}{2}}}(x)$$
+
+where $n = 0$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Spherical Bessel Function of the First Kind of Order 1
+
+```Python
+spherical_bessel_j_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Spherical Bessel function of the first kind:
+
+$$j_{n}(x)={\sqrt{\frac{\pi}{2x}}}J_{n + {\frac{1}{2}}}(x)$$
+
+where $n = 1$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Spherical Bessel Function of the Second Kind
+
+```Python
+spherical_bessel_y(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Spherical Bessel function of the second kind:
+
+$$y_{n}(x)={\sqrt{\frac{\pi}{2x}}}Y_{n+{\frac{1}{2}}}(x).$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Spherical Bessel Function of the Second Kind of Order 0
+
+```Python
+spherical_bessel_y_0(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Spherical Bessel function of the second kind:
+
+$$y_{n}(x)={\sqrt{\frac{\pi}{2x}}}Y_{n+{\frac{1}{2}}}(x)$$
+
+where $n = 0$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Spherical Bessel Function of the Second Kind of Order 1
+
+```Python
+spherical_bessel_y_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Spherical Bessel function of the second kind:
+
+$$y_{n}(x)={\sqrt{\frac{\pi}{2x}}}Y_{n+{\frac{1}{2}}}(x)$$
+
+where $n = 1$.
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Spherical Hankel Functions
+
+#### Spherical Hankel Function of the First Kind
+
+```Python
+spherical_hankel_h_1(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Spherical Hankel function of the first kind:
+
+$$h_{n}^{1}(z)=\frac{\sqrt{\frac{\pi}{2}}H_{n +\frac{1}{2}}^{1}(z)}{\sqrt{z}},$$
+
+where $H_{n}^{1}$ is the Hankel function of the first kind.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Spherical Hankel Function of the Second Kind
+
+```Python
+spherical_hankel_h_2(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Spherical Hankel function of the second kind:
+
+$$h_{n}^{2}(z)=\frac{\sqrt{\frac{\pi}{2}}H_{n+\frac{1}{2}}^{2}(z)}{\sqrt{z}},$$
+
+where $H_{n}^{2}$ is the Hankel function of the second kind.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Modified Spherical Bessel Functions
+
+#### Modified Spherical Bessel Function of the First Kind
+
+```Python
+modified_spherical_bessel_i(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Modified spherical Bessel function of the first kind:
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Spherical Bessel Function of the First Kind of Order 0
+
+```Python
+modified_spherical_bessel_i_0(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Spherical Bessel Function of the First Kind of Order 1
+
+```Python
+modified_spherical_bessel_i_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Spherical Bessel Function of the Second Kind
+
+```Python
+modified_spherical_bessel_k(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Spherical Bessel Function of the Second Kind of Order 0
+
+```Python
+modified_spherical_bessel_k_0(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Spherical Bessel Function of the Second Kind of Order 1
+
+```Python
+modified_spherical_bessel_k_1(
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) – input.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Kelvin Functions
+
+#### Kelvin Function of the First Kind ($\operatorname{ber}$)
+
+```Python
+kelvin_ber(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$$\mathrm {ber} _{n}(x)=({\frac {x}{2}})^{n}\sum _{k\geq 0}{\frac {\cos [({\frac {3n}{4}}+{\frac {k}{2}})\pi ]}{k!\Gamma (n+k+1)}}({\frac {x^{2}}{4}})^{k}.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Kelvin Function of the First Kind ($\operatorname{bei}$)
+
+```Python
+kelvin_bei(
+    n: Tensor,
+    z: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Kelvin Function of the Second Kind ($\operatorname{kei}$)
+
+```Python
+kelvin_kei(
+    n: Tensor,
+    z: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Kelvin Function of the Second Kind ($\operatorname{ker}$)
+
+```Python
+kelvin_ker(
+    n: Tensor,
+    z: Tensor,
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – order. If $z$ is a number, $n$ must be a tensor.
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor) *or Number*) – input. If $z$ is a number, $n$ must be a tensor.
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Struve and Modified Struve Functions
+
+#### Struve Function
+
+```Python
+struve_h(
+    n: Tensor, 
+    z: Tensor, 
+    *,
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Struve function:
+
+$$\mathbf{H}_{n}(z) = \sum_{m = 0}^{\infty}{\frac {(-1)^{m}}{\Gamma (m+{\frac {3}{2}})\Gamma (m+n +{\frac {3}{2}})}}({\frac {z}{2}})^{2m+n +1}.$$
+
+where $\Gamma(z)$ is the gamma function.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Modified Struve Function
+
+```Python
+struve_l(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Modified Struve function:
+
+$$\mathbf {L} _{n }(z)=\sum _{m=0}^{\infty }{\frac {1}{\Gamma (m+{\frac {3}{2}})\Gamma (m+n +{\frac {3}{2}})}}({\frac {z}{2}})^{2m+n +1}.$$
+
+where $\Gamma(z)$ is the gamma function.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Lommel Functions
+
+#### Lommel Function of the First Kind
+
+#### Lommel Function of the Second Kind
+
+### Anger and Weber Functions
+
+#### Anger Function
+
+```Python
+anger_j(
+    n: Tensor,
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Anger function:
+
+$$\mathbf{J}_{n}(z)={\frac{1}{\pi}}\int_{0}^{\pi}\cos(n\theta-z\sin\theta)d\theta.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Weber Function
+
+```Python
+weber_e(
+    n: Tensor,
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Weber function:
+
+$$\mathbf{E}_{n}(z)={\frac{1}{\pi}}\int_{0}^{\pi}\sin(n\theta-z\sin \theta )d\theta.$$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Parabolic Cylinder Function
+
+```Python
+parabolic_cylinder_d(
+    n: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None
+) -> Tensor
+```
+
+Parabolic cylinder function:
+
+$$D_{n}(z) = \sqrt{\pi} 2^{\tfrac{n}{2}} e^{-\frac{z^2}{4}} \left(\frac{ _1F_1(-\frac{n }{2}; \frac{1}{2}; \frac{z^2}{2})}{\Gamma (\frac{1-n }{2})}-\frac{\sqrt{2} z  _1F_1(\frac{1-n }{2};\frac{3}{2};\frac{z^2}{2})}{\Gamma (-\frac{n }{2})} \right),$$
+
+where $_1F_1$ is the confluent hypergeometric function of the first kind and $\Gamma$ is the gamma function.
+
+### Confluent Hypergeometric Functions
+
+#### Confluent Hypergeometric Function of the First Kind
+
+```Python
+confluent_hypergeometric_1_f_1(
+    a: Tensor,
+    b: Tensor,
+    z: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Confluent hypergeometric function of the first kind:
+
+$$_{1}{F}_{1}(a; b; z) = \sum_{k = 0}^{\infty} \frac{a_{k}}{b_{k}} \frac{z^{k}}{k!},$$
+
+where $a_{k}$ and $b_{k}$ are rising factorials.
+
+#### Confluent Hypergeometric Function of the Second Kind
+
+### Whittaker Functions
+
+Whittaker functions are defined as a special solution of Whittaker’s equation:
+
+$${\frac  {d^{2}w}{dz^{2}}}+(-{\frac  {1}{4}}+{\frac  {\kappa }{z}}+{\frac  {1/4-\mu ^{2}}{z^{2}}})w=0.$$
+
+#### Whittaker Function ($M_{\kappa, \mu}$)
+
+```Python
+whittaker_m(
+    k: Tensor,
+    m: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Whittaker function:
+
+$${\displaystyle M_{\kappa ,\mu }(z)=\exp (-z/2)z^{\mu +{\tfrac {1}{2}}}M(\mu -\kappa +{\tfrac {1}{2}},1+2\mu ,z)}.$$
+
+##### Parameters
+
+**k** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**m** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Whittaker Function ($W_{\kappa, \mu}$)
+
+```Python
+whittaker_w(
+    k: Tensor,
+    m: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Whittaker function:
+
+$${\displaystyle W_{\kappa ,\mu }(z)=\exp (-z/2)z^{\mu +{\tfrac {1}{2}}}U(\mu -\kappa +{\tfrac {1}{2}},1+2\mu ,z).}$$
+
+##### Parameters
+
+**k** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**m** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Legendre Functions
+
+#### Legendre Function of the First Kind
+
+#### Legendre Function of the Second Kind
+
+### Associated Legendre Functions
+
+#### Associated Legendre Function of the First Kind
+
+#### Associated Legendre Function of the Second Kind
+
+### Ferrers Functions
+
+#### Ferrers Function of the First Kind
+
+#### Ferrers Function of the Second Kind
+
+### Spherical and Spheroidal Harmonics
+
+### Generalized Hypergeometric and Related Functions
+
+### Appell Functions
+
+#### Appell Function ($F_{1}$)
+
+```Python
+appell_f_1(
+    a: Tensor, 
+    b: Tensor,
+    c: Tensor,
+    d: Tensor,
+    x: Tensor,
+    y: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Appell function:
+
+$$F_{1}(a; b, c; d; x, y) = \sum_{m, n=0}^{\infty}{\frac{a_{m + n}b_{m}c_{n}}{d_{m + n}m!n!}}x^{m}y^{n}.$$
+
+##### Parameters
+
+**a** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**b** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**c** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**d** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Appell Function ($F_{2}$)
+
+```Python
+appell_f_2(
+    a: Tensor, 
+    b: Tensor,
+    c: Tensor,
+    d: Tensor,
+    e: Tensor,
+    x: Tensor,
+    y: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**a** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**b** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**c** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**d** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**e** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Appell Function ($F_{3}$)
+
+```Python
+appell_f_3(
+    a: Tensor, 
+    b: Tensor,
+    c: Tensor,
+    d: Tensor,
+    e: Tensor,
+    x: Tensor,
+    y: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**a** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**b** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**c** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**d** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**e** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Appell Function ($F_{4}$)
+
+```Python
+appell_f_4(
+    a: Tensor, 
+    b: Tensor,
+    c: Tensor,
+    d: Tensor,
+    x: Tensor,
+    y: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**a** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**b** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**c** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**d** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### $q$-Hypergeometric and Related Functions
+
+#### $q$-Factorial
+
+#### $q$-Binomial Coefficient
+
+#### $q$-Gamma Function
+
+#### $q$-Digamma Function
+
+#### $q$-Polygamma Function
+
+### Chebyshev Polynomials
+
+#### Chebyshev Polynomial of the First Kind
+
+```Python
+chebyshev_polynomial_t(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Chebyshev polynomial of the first kind, $T_{n}(x).$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Chebyshev Polynomial of the Second Kind
+
+```Python
+chebyshev_polynomial_u(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Chebyshev polynomial of the second kind, $U_{n}(x).$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Chebyshev Polynomial of the Third Kind
+
+```Python
+chebyshev_polynomial_v(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Chebyshev polynomial of the third kind, $V_{n}(x).$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Chebyshev Polynomial of the Fourth Kind
+
+```Python
+chebyshev_polynomial_w(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Chebyshev polynomial of the fourth kind, $W_{n}(x).$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Shifted Chebyshev Polynomials
+
+#### Shifted Chebyshev Polynomial of the First Kind
+
+```Python
+shifted_chebyshev_polynomial_t(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Shifted Chebyshev polynomial of the first kind, $T_{n}^{\ast}(x).$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Shifted Chebyshev Polynomial of the Second Kind
+
+```Python
+shifted_chebyshev_polynomial_u(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Shifted Chebyshev polynomial of the second kind, $U_{n}^{\ast}(x).$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Shifted Chebyshev Polynomial of the Third Kind
+
+```Python
+shifted_chebyshev_polynomial_v(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Shifted Chebyshev polynomial of the third kind, $V_{n}^{\ast}(x).$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Shifted Chebyshev Polynomial of the Fourth Kind
+
+```Python
+shifted_chebyshev_polynomial_w(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Shifted Chebyshev polynomial of the fourth kind, $W_{n}^{\ast}(x).$
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Hermite Polynomials
+
+#### Probabilist’s Hermite Polynomial
+
+```Python
+hermite_polynomial_he(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Probabilist’s Hermite polynomial:
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Physicist’s Hermite Polynomial
+
+```Python
+hermite_polynomial_h(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Physicist’s Hermite polynomial:
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Orthogonal Polynomials
+
+### Legendre Forms of Elliptic Integrals
+
+#### Elliptic Integral of the First Kind
+
+```Python
+legendre_elliptic_integral_f(
+    m: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Legendre form of the incomplete elliptic integral of the first kind:
+
+The incomplete elliptic integral is defined in terms of the parameter $m$ instead of the elliptic modulus $k$. $m$ is defined as $m = k^{2}$.
+
+##### Parameters
+
+**m** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Elliptic Integral of the Second Kind
+
+```Python
+legendre_elliptic_integral_e(
+    m: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Legendre form of the incomplete elliptic integral of the second kind:
+
+The incomplete elliptic integral is defined in terms of the parameter $m$ instead of the elliptic modulus $k$. $m$ is defined as $m = k^{2}$.
+
+##### Parameters
+
+**m** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Elliptic Integral of the Third Kind
+
+```Python
+legendre_elliptic_integral_pi(
+    n: Tensor, 
+    m: Tensor, 
+    z: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Legendre form of the incomplete elliptic integral of the third kind:
+
+The incomplete elliptic integral is defined in terms of the parameter $m$ instead of the elliptic modulus $k$. $m$ is defined as $m = k^{2}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**m** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Legendre Forms of Complete Elliptic Integrals
+
+#### Complete Elliptic Integral of the First Kind
+
+```Python
+complete_legendre_elliptic_integral_k(
+    m: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Legendre form of the complete elliptic integral of the first kind:
+
+$$K(m) = F({\tfrac{\pi}{2}}, m).$$
+
+The complete elliptic integral is defined in terms of the parameter $m$ instead of the elliptic modulus $k$. $m$ is defined as $m = k^{2}$.
+
+##### Parameters
+
+**m** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Complete Elliptic Integral of the Second Kind
+
+```Python
+complete_legendre_elliptic_integral_e(
+    m: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Legendre form of the complete elliptic integral of the second kind:
+
+$$E(m) = \int_{0}^{\tfrac{\pi}{2}}{\sqrt{1 - m \sin^{2} \theta}}d\theta.$$
+
+The complete elliptic integral is defined in terms of the parameter $m$ instead of the elliptic modulus $k$. $m$ is defined as $m = k^{2}$.
+
+##### Parameters
+
+**m** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Complete Elliptic Integral of the Third Kind
+
+```Python
+complete_legendre_elliptic_integral_pi(
+    n: Tensor, 
+    m: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Legendre form of the complete elliptic integral of the third kind:
+
+$$\Pi(n, m) = \int_{0}^{\frac{\pi}{2}}{\frac{d\theta}{(1 - n\sin^{2}\theta){\sqrt{1 - m\sin ^{2}\theta }}}}.$$
+
+The complete elliptic integral is defined in terms of the parameter $m$ instead of the elliptic modulus $k$. $m$ is defined as $m = k^{2}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**m** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Carlson Symmetric Forms of Elliptic Integrals
+
+#### Carlson Elliptic Integral ($R_{C}$)
+
+```Python
+carlson_elliptic_integral_r_c(
+    x: Tensor, 
+    y: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Carlson Elliptic Integral ($R_{D}$)
+
+```Python
+carlson_elliptic_integral_r_d(
+    x: Tensor, 
+    y: Tensor,
+    z: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Carlson Elliptic Integral ($R_{E}$)
+
+```Python
+carlson_elliptic_integral_r_e(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Carlson Elliptic Integral ($R_{F}$)
+
+```Python
+carlson_elliptic_integral_r_f(
+    x: Tensor, 
+    y: Tensor,
+    z: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Carlson Elliptic Integral ($R_{G}$)
+
+```Python
+carlson_elliptic_integral_r_g(
+    x: Tensor, 
+    y: Tensor,
+    z: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Carlson Elliptic Integral ($R_{J}$)
+
+```Python
+carlson_elliptic_integral_r_j(
+    x: Tensor, 
+    y: Tensor,
+    z: Tensor,
+    p: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**y** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Carlson Elliptic Integral ($R_{K}$)
+
+```Python
+carlson_elliptic_integral_r_k(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Carlson Elliptic Integral ($R_{M}$)
+
+```Python
+carlson_elliptic_integral_r_m(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+### Theta Functions
+
+#### Theta Function ($\theta_{1}$)
+
+```Python
+theta_1(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Theta Function ($\theta_{2}$)
+
+```Python
+theta_2(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Theta Function ($\theta_{3}$)
+
+```Python
+theta_3(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Theta Function ($\theta_{4}$)
+
+```Python
+theta_4(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+### Jacobi Elliptic Functions
+
+#### Jacobi Amplitude Function
+
+```Python
+jacobi_amplitude_am(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Jacobi Elliptic Function ($\operatorname{sn}$)
+
+```Python
+jacobi_elliptic_sn(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$$\operatorname{sn}(z \mid m) = \sin(\operatorname{am}(z \mid m))$$
+
+#### Jacobi Elliptic Function ($\operatorname{cn}$)
+
+```Python
+jacobi_elliptic_cn(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$$\operatorname{cn}(z \mid m) = \cos(\operatorname{am}(z \mid m))$$
+
+#### Jacobi Elliptic Function ($\operatorname{dn}$)
+
+```Python
+jacobi_elliptic_dn(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Jacobi Elliptic Function ($\operatorname{sd}$)
+
+```Python
+jacobi_elliptic_sd(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Jacobi Elliptic Function ($\operatorname{cd}$)
+
+```Python
+jacobi_elliptic_cd(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$$\operatorname{cd}(z \mid m) = \frac{\operatorname{cn}(z \mid m)}{\operatorname{dn}(z \mid m)}$$
+
+#### Jacobi Elliptic Function ($\operatorname{sc}$)
+
+```Python
+jacobi_elliptic_sc(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+### Inverse Jacobi Elliptic Functions
+
+#### Inverse Jacobi Elliptic Function ($\operatorname{sn}$)
+
+```Python
+inverse_jacobi_elliptic_sn(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Inverse Jacobi Elliptic Function ($\operatorname{cn}$)
+
+```Python
+inverse_jacobi_elliptic_cn(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Inverse Jacobi Elliptic Function ($\operatorname{dn}$)
+
+```Python
+inverse_jacobi_elliptic_dn(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Inverse Jacobi Elliptic Function ($\operatorname{sd}$)
+
+```Python
+inverse_jacobi_elliptic_sd(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Inverse Jacobi Elliptic Function ($\operatorname{cd}$)
+
+```Python
+inverse_jacobi_elliptic_cd(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Inverse Jacobi Elliptic Function ($\operatorname{sc}$)
+
+```Python
+inverse_jacobi_elliptic_sc(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+### Weierstrass Elliptic Functions
+
+#### Weierstrass Elliptic Function (p)
+
+#### Weierstrass Elliptic Function (\zeta)
+
+#### Weierstrass Elliptic Function (\sigma)
+
+### Modular Functions
+
+#### Elliptic Function (\lambda)
+
+#### Klein’s Complete Invariant Function
+
+### Bernoulli Number and Polynomial
+
+#### Bernoulli Number
+
+```Python
+bernoulli_number_b(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ Bernoulli number, $B_{n}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Bernoulli Polynomial
+
+```Python
+bernoulli_polynomial_b(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Bernoulli polynomial, $B_{n}(x)$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**x** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Euler Number and Polynomial
+
+#### Euler Number
+
+```Python
+euler_number_e(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ Euler number, $E_{n}$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+#### Euler Polynomial
+
+```Python
+euler_polynomial_e(
+    n: Tensor, 
+    x: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Euler polynomial, $E_{n}(x)$.
+
+##### Parameters
+
+**n** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+**z** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor)) –
+
+##### Keyword Arguments
+
+**out** ([Tensor](https://pytorch.org/docs/stable/tensors.html#torch.Tensor), *optional*) – output.
+
+### Zeta and Related Functions
+
+#### Riemann Zeta Function
+
+```Python
+riemann_zeta(
+    s: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Riemann zeta function:
+
+$$\zeta(s)=\sum _{n=1}^{\infty}{\frac{1}{n^{s}}}.$$
+
+#### Hurwitz Zeta Function
+
+```Python
+hurwitz_zeta(
+    s: Tensor,
+    a: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Hurwitz zeta function:
+
+$$\zeta(s, a) = \sum _{n = 0}^{\infty}{\frac{1}{(n + a)^{s}}}.$$
+
+#### Polylogarithm
+
+```Python
+polylogarithm_li(
+    s: Tensor,
+    z: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+Polylogarithm:
+
+$$\operatorname{Li}_{s + 1}(z ) = \int_{0}^{z}{\frac{\operatorname{Li}_{s}(t)}{t}}dt.$$
+
+#### Lerch Zeta Function
+
+```Python
+lerch_zeta_l(
+    l: Tensor,
+    z: Tensor,
+    a: Tensor,
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+#### Lerch Transcendent
+
+#### Dirichlet L-Function
+
+### Multiplicative Number Theoretic Functions
+
+#### Prime Number
+
+```Python
+prime_number_p(
+    n: Tensor, 
+    *, 
+    out: Optional[Tensor] = None,
+) -> Tensor
+```
+
+$n^{\text{th}}$ prime number, $p(n)$.
+
+#### Euler’s Totient Function
+
+#### Divisor Function
+
+#### Jordan’s Totient Function
+
+#### Möbius Function
+
+#### Liouville Function
+
+### Matthieu Characteristic Values
+
+#### Matthieu Characteristic Value ($a$)
+
+#### Matthieu Characteristic Value ($b$)
+
+### Angular Matthieu Functions
+
+#### Angular Matthieu Function ($\operatorname{ce}$)
+
+#### Angular Matthieu Function ($\operatorname{se}$)
+
+### Radial Mathieu Functions
+
+#### Radial Matthieu Function ($\operatorname{M}c$)
+
+#### Radial Matthieu Function ($\operatorname{M}s$)
+
+### Lamé Functions
+
+### Spherodial Wave Functions
+
+### Heun Functions
+
+#### Heun Function
+
+#### Confluent Heun Function
+
+#### Doubly-Confluent Heun Function
+
+#### Bi-Confluent Heun Function
+
+#### Tri-Confluent Heun Function
+
+### Painlevé Transcendents
+
+### Coulomb Wave Functions
+
+#### Coulomb Wave Function (F)
+
+#### Coulomb Wave Function (G)
+
+### 3-j, 6-j, and 9-j Symbols
+
+#### 3-j Symbol
+
+#### 6-j Symbol
+
+#### 9-j Symbol
+
+## Metrics
+
+<details>
+What are the main metrics to measure the value of this feature?
+</details>
+
+## Drawbacks
+
+<details>
+Are there any reasons why we should not do this? Here we aim to evaluate risk and check ourselves.
+
+Please consider:
+* is it a breaking change?
+* Impact on UX
+* implementation cost, both in terms of code size and complexity
+* integration of this feature with other existing and planned features
+</details>
+
+## Alternatives
+
+<details>
+What other designs have been considered? What is the impact of not doing this?
+</details>
+
+## Prior Art
+
+<details>
+Discuss prior art (both good and bad) in relation to this proposal:
+* Does this feature exist in other libraries? What experience has their community had?
+* What lessons can be learned from other implementations of this feature?
+* Published papers or great posts that discuss this
+</details>
+
+### Cephes Mathematical Library
+
+Suite of elementary and special functions written by Stephen L. Moshier. It was initially created as a supplement to his numerical analysis textbook, “Methods and Programs for Mathematical Functions.” Unsure of the original publication date, but I estimate somewhere between 1984 and 1986. It was most recently updated, by Moshier, in 2018. Its use is ubiquitous (it’s even presently used in PyTorch), and DeepMind recently maintained a library wrapper for PyTorch.
+
+### specfun
+
+Suite of elementary and special functions authored by W. J. Cody, a numerical analysis pioneer, written in Fortran. It’s abandonware.
+
+### Wolfram Language
+
+General-purpose, commercial, multi-paradigm programming language written and maintained by Wolfram Research. The Wolfram Language touts one of the best suites of elementary and special functions. Most of these functions support either symbolic, or relevant to PyTorch, numerical evaluation and differentiation.
+
+### MATLAB
+### International Mathematics and Statistics Library (IMSL)
+### NAG Numerical Library
+### GNU Octave
+### GNU Scientific Library (GSL)
+
+### SciPy
+
+SciPy is a free and open-source Python package for scientific computing. It contains modules for linear algebra, integration, optimization, etc. SciPy also contains a robust suite of special functions. Most of the special function implementations rely on third-party packages, many featured elsewhere in this subsection (e.g., Cephes and specfun).
+
+## How we teach this
+
+<details>
+* What names and terminology work best for these concepts and why? How is this idea best presented?
+* Would the acceptance of this proposal mean the PyTorch documentation must be re-organized or altered?
+* How should this feature be taught to existing PyTorch users?
+</details>
+
+## Unresolved questions
+
+<details>
+* What parts of the design do you expect to resolve through the RFC process before this gets merged?
+* What parts of the design do you expect to resolve through the implementation of this feature before stabilization?
+* What related issues do you consider out of scope for this RFC that could be addressed in the future independently of the solution that comes out of this RFC?
+</details>
+
+## Resolution
+
+<details>
+We decided to do it. X% of the engineering team actively approved of this change.
+</details>
+
+### Level of Support
+
+<details>
+Choose one of the following:
+* 1: Overwhelming positive feedback.
+* 2: Positive feedback.
+* 3: Majority Acceptance, with conflicting Feedback.
+* 4: Acceptance, with Little Feedback.
+* 5: Unclear Resolution.
+* 6: RFC Rejected.
+* 7: RFC Rejected, with Conflicting Feedback.
+</details>
+
+#### Additional Context
+
+<details>
+Some people were in favor of it, but some people didn’t want it for project X.
+</details>
+
+### Next Steps
+
+<details>
+Will implement it.
+</details>
+
+#### Tracking issue
+
+<details>
+<github issue URL>
+</details>
+
+#### Exceptions
+
+<details>
+Not implementing on project X now. Will revisit the decision in 1 year.
+</details>
\ No newline at end of file