PolyGamma

PolyGamma[z] gives the digamma function .

PolyGamma[n, z] gives the derivative of the digamma function .

PolyGamma[z] is the logarithmic derivative of the gamma function, given by .

PolyGamma[n, z] is given by .

The digamma function is ; is the logarithmic derivative of the gamma function.

PolyGamma[z] and PolyGamma[n, z] are meromorphic functions of z with no branch cut discontinuities.

FullSimplify and FunctionExpand include transformation rules for PolyGamma.

See The Mathematica Book: Section 3.2.10.

Implementation Notes: see section A.9.4.

See also: Gamma, LogGamma, EulerGamma.

Further Examples