Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions > Gamma Functions and Related Functions >
Built-in Mathematica SymbolTutorials »|See Also »|More About »

PolyGamma

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.
New in 1 | Last modified in 6
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team