pytorch/torch/csrc/api
Allen Goodman 18273c39da Physicist’s Hermite polynomial (#78352)
Adds:

```Python
hermite_polynomial_h(input, n, *, out=None) -> Tensor
```
Physicist’s Hermite polynomial $H_{n}(\text{input})$.

If $n = 0$, $1$ is returned. If $n = 1$, $\text{input}$ is returned. Otherwise, the recursion:

$$H_{n + 1}(\text{input}) = 2 \times \text{input} \times H_{n}(\text{input}) - H_{n - 1}(\text{input})$$

is evaluated.

## Derivatives

Recommended $k$-derivative formula with respect to $\text{input}$:

$$\frac{d^{k}}{d \times \text{input}^{k}} H_{n}^{(k)} = 2^{k} \times \frac{n!}{(n - k)!}H_{n - k}(\text{input})$$
Pull Request resolved: https://github.com/pytorch/pytorch/pull/78352
Approved by: https://github.com/mruberry
2022-05-28 02:26:30 +00:00
..
include/torch Physicist’s Hermite polynomial (#78352) 2022-05-28 02:26:30 +00:00
src T112685841: Use irange in PyTorch (#73378) 2022-02-26 06:34:22 +00:00