LGAMMA(3M) — MATHEMATICAL LIBRARY

NAME

lgamma, gamma − log gamma function

SYNOPSIS

#include <math.h>

extern int signgam;

double lgamma(double x);

DESCRIPTION

lgamma() returns

ln|Γ(x)|
where
Γ(x) = ∫0s10∞tx−1e−tdt
for x > 0 and
Γ(x) = π/(Γ(1−x)sin(πx))
for x < 1.

lgamma() uses the external integer signgam to return the sign of Γ(x).

IDIOSYNCRASIES

In the case of lgamma(), do not use the expression signgam∗exp(lgamma(x)) to compute ‘g := Γ(x)’. Instead compute lgamma() first:

lg = lgamma(x); g = signgam∗exp(lg);

only after lgamma() has returned can signgam be correct. Note that Γ(x) must overflow when x is large enough, underflow when −x is large enough, and generate a division by 0 exception at the singularities x a nonpositive integer.

RETURN VALUES

For exceptional cases, matherr(3M) tabulates the values to be returned as dictated by various Standards.

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