code: def polygamma(n, x):
      r"""Polygamma functions.
  
      Defined as :math:`\psi^{(n)}(x)` where :math:`\psi` is the
      `digamma` function. See [dlmf]_ for details.
  
      Parameters
      ----------
      n : array_like
          The order of the derivative of the digamma function; must be
          integral
      x : array_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)
  
      """
      n, x = asarray(n), asarray(x)
      fac2 = (-1.0) ** (n + 1) * gamma(n + 1.0) * zeta(n + 1, x)
      return where(n == 0, psi(x), fac2)
  
imports: import operator
  import numpy
  import math
  from numpy import pi, asarray, floor, isscalar, iscomplex, real, imag, sqrt, where, mgrid, sin, place, issubdtype, extract, inexact, nan, zeros, sinc
  from .None import _ufuncs
  from ._ufuncs import mathieu_a, mathieu_b, iv, jv, gamma, psi, hankel1, hankel2, yv, kv, ndtri, poch, binom, hyp0f1
  from .None import specfun
  from .None import orthogonal
  from ._comb import _comb_int
label_desc: Use image node_id 26 for calling a global function with example usage: polygamma(n, x) and returns: where