tgamma (3) - Linux Man Pages
tgamma: true gamma function
NAME
tgamma, tgammaf, tgammal - true gamma function
SYNOPSIS
#include <math.h>
double tgamma(double x);
float tgammaf(float x);
long double tgammal(long double x);
Link with -lm.
Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
tgamma(), tgammaf(), tgammal():
- _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
DESCRIPTION
These functions calculate the Gamma function of x.The Gamma function is defined by
- Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
It is defined for every real number except for nonpositive integers. For nonnegative integral m one has
- Gamma(m+1) = m!
and, more generally, for all x:
- Gamma(x+1) = x * Gamma(x)
Furthermore, the following is valid for all values of x outside the poles:
- Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
RETURN VALUE
On success, these functions return Gamma(x).If x is a NaN, a NaN is returned.
If x is positive infinity, positive infinity is returned.
If x is a negative integer, or is negative infinity, a domain error occurs, and a NaN is returned.
If the result overflows, a range error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct mathematical sign.
If the result underflows, a range error occurs, and the functions return 0, with the correct mathematical sign.
If x is -0 or +0, a pole error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign as the 0.
ERRORS
See math_error(7) for information on how to determine whether an error has occurred when calling these functions.The following errors can occur:
- Domain error: x is a negative integer, or negative infinity
- errno is set to EDOM. An invalid floating-point exception (FE_INVALID) is raised (but see BUGS).
- Pole error: x is +0 or -0
- errno is set to ERANGE. A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
- Range error: result overflow
- errno is set to ERANGE. An overflow floating-point exception (FE_OVERFLOW) is raised.
glibc also gives the following error which is not specified in C99 or POSIX.1-2001.
- Range error: result underflow
- An underflow floating-point exception (FE_UNDERFLOW) is raised, and errno is set to ERANGE.
VERSIONS
These functions first appeared in glibc in version 2.1.ATTRIBUTES
For an explanation of the terms used in this section, see attributes(7).Interface | Attribute | Value |
tgamma(), tgammaf(), tgammal() | Thread safety | MT-Safe |
CONFORMING TO
C99, POSIX.1-2001, POSIX.1-2008.NOTES
This function had to be called "true gamma function" since there is already a function gamma(3) that returns something else (see gamma(3) for details).BUGS
Before version 2.18, the glibc implementation of these functions did not set errno to EDOM when x is negative infinity.Before glibc 2.19, the glibc implementation of these functions did not set errno to ERANGE on an underflow range error. x
In glibc versions 2.3.3 and earlier, an argument of +0 or -0 incorrectly produced a domain error (errno set to EDOM and an FE_INVALID exception raised), rather than a pole error.
SEE ALSO
gamma(3), lgamma(3)COLOPHON
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