PolyGamma

PolyGamma[z]
gives the digamma function .

PolyGamma[n, z]
gives the n^(th) derivative of the digamma function .

DetailsDetails

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • PolyGamma[z] is the logarithmic derivative of the gamma function, given by .
  • PolyGamma[n, z] is given for positive integer by .
  • For arbitrary complex n the polygamma function is defined by fractional calculus analytic continuation.
  • PolyGamma[z] and PolyGamma[n, z] are meromorphic functions of z with no branch cut discontinuities.
  • For certain special arguments, PolyGamma automatically evaluates to exact values.
  • PolyGamma can be evaluated to arbitrary numerical precision.
  • PolyGamma automatically threads over lists.
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