scipy.special.

polygamma#

scipy.special.polygamma(n, x)[source]#

Polygamma functions.

Defined as \(\psi^{(n)}(x)\) where \(\psi\) is the digamma function. See [dlmf] for details.

Parameters:

narray_like: The order of the derivative of the digamma function; must be integral
xarray_like: Real valued input

Returns:

ndarray: Function results

See also

digamma

Notes

polygamma has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	✅
JAX	✅	✅
Dask	✅	n/a

See Support for the array API standard for more information.

References

[dlmf]

NIST, Digital Library of Mathematical Functions, https://dlmf.nist.gov/5.15

Examples

>>> from scipy import special
>>> x = [2, 3, 25.5]
>>> special.polygamma(1, x)
array([ 0.64493407,  0.39493407,  0.03999467])
>>> special.polygamma(0, x) == special.psi(x)
array([ True,  True,  True], dtype=bool)