digammainv

mpsci.fun.digammainv(y)

Inverse of the digamma function (real values only).

The digamma function [1] [2] is the logarithmic derivative of the gamma function.

For real y, digammainv(y) returns the positive x such that digamma(x) = y.

The digamma function is also known as \(\psi_{0}\); mpmath.digamma(x) is the same as mpmath.psi(0, x).

References

[1]

“Digamma function”, https://en.wikipedia.org/wiki/Digamma_function

[2]

Abramowitz and Stegun, Handbook of Mathematical Functions (section 6.3), Dover Publications, New York (1972).

Examples

>>> from mpmath import mp
>>> from mpsci.fun import digammainv
>>> mp.dps = 25
>>> y = mpmath.mpf('7.89123')
>>> y
mpf('7.891230000000000000000000011')
>>> x = digammainv(y)
>>> x
mpf('2674.230572001301673812839151')
>>> mp.digamma(x)
mpf('7.891230000000000000000000011')