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PolyGamma

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PolyGamma[z]
gives the digamma function psi(z).
PolyGamma[n, z]
gives the n^(th) derivative of the digamma function psi^((n))(z).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • PolyGamma[z] is the logarithmic derivative of the gamma function, given by psi(z)=Gamma^′(z)/Gamma(z).
  • PolyGamma[n, z] is given for positive integer n by psi^((n))(z)=d^npsi(z)/dz^n.
  • 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.
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