multivariate_logbeta

mpsci.fun.multivariate_logbeta(alpha)

Logarithm of the multivariate beta function.

The multivariate beta function for the vector \(\alpha\) is

\[B(\alpha) = \frac{\sum_{k}\Gamma(\alpha_{k})}{\Gamma(\sum_{k}\alpha_{k})}\]

where \(\Gamma(z)\) is the Gamma function.

Examples

>>> from mpmath import mp
>>> mp.dps = 25
>>> from mpsci.fun import multivariate_logbeta

>>> multivariate_logbeta([1.5, 2.0, 4.0, 1.25, 5.0])
mpf('-17.15300326630985105656599532')