gives the digamma function .
gives the n derivative of the digamma function .
- 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.
Examplesopen allclose all
Introduced in 1988
(1.0)| Updated in 2007