scipy.special.polygamma

scipy.special.polygamma(n, x)

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

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)