NAME

gamma, lgamma, signgam − log gamma function

SYNOPSIS

#include <math.h>

double gamma (x)
double x;

double lgamma (x)
double x;

extern int signgam;

DESCRIPTION

Gamma returns ln(|Γ( x)|), whereΓ( x) is defined as ∞∫0e−ttx−1dt.  The sign of Γ( x)is returned in the external integer signgam. The argument x must not be a non-positive integer.  (Gamma is defined over the reals excluding the non-positive integers). 

The following C program fragment can be used to calculate Γ:

if ((y = gamma(x)) > LN_MAXDOUBLE)
error();
y = signgam ∗ exp(y);

where if y is greater than LN_MAXDOUBLE, as defined in the <values.h> header file, exp(3M) will return a range error.

ERRORS

Series 300
For non-positive integer arguments gamma returns HUGE_VAL and sets errno to EDOM.  A message indicating SING error is printed on the standard error output. 

If the correct value would overflow, gamma returns HUGE_VAL and sets errno to ERANGE. 

Series 800 (/lib/libm.a)
For non-positive integer arguments, gamma returns HUGE_VAL and sets errno to EDOM.  A message indicating SING error is printed on the standard error output. 

If the correct value would overflow, gamma returns HUGE_VAL and sets errno to ERANGE. 

Gamma returns NaN and sets errno to EDOM when x is NaN, or returns +INFINITY and sets errno to EDOM when x is ±INFINITY .  A message indicating DOMAIN error is printed on the standard error output. 

Series 800 (ANSI C /lib/libM.a)
No error messages are printed on the standard error output.

For non-positive integer arguments gamma returns HUGE_VAL and sets errno to EDOM.  A message indicating SING error is printed on the standard error output. 

If the correct value would overflow, gamma returns HUGE_VAL and sets errno to ERANGE. 

Gamma returns NaN and sets errno to EDOM when x is NaN, or returns +INFINITY and sets errno to EDOM when x is ±INFINITY . 

These error-handling procedures may be changed with the function matherr(3M).

SEE ALSO

exp(3M), isinf(3M), isnan(3M), matherr(3M), values(5). 

STANDARDS CONFORMANCE

gamma: SVID2, XPG2, XPG3

signgam: SVID2, XPG2, XPG3

Hewlett-Packard Company  —  HP-UX Release 7.0: Sept 1989