NAME  SYNOPSIS  DESCRIPTION  RETURN VALUE  ERRORS  VERSIONS  ATTRIBUTES  CONFORMING TO  NOTES  BUGS  SEE ALSO  COLOPHON 

TGAMMA(3) Linux Programmer's Manual TGAMMA(3)
tgamma, tgammaf, tgammal  true gamma function
#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
These functions calculate the Gamma function of x. The Gamma function is defined by Gamma(x) = integral from 0 to infinity of t^(x1) 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)
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.
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 floatingpoint exception (FE_INVALID) is raised (but see BUGS). Pole error: x is +0 or 0 errno is set to ERANGE. A dividebyzero floatingpoint exception (FE_DIVBYZERO) is raised. Range error: result overflow errno is set to ERANGE. An overflow floatingpoint exception (FE_OVERFLOW) is raised. glibc also gives the following error which is not specified in C99 or POSIX.12001. Range error: result underflow An underflow floatingpoint exception (FE_UNDERFLOW) is raised. errno is not set for this case.
These functions first appeared in glibc in version 2.1.
For an explanation of the terms used in this section, see attributes(7). ┌───────────────────────────────┬───────────────┬─────────┐ │Interface │ Attribute │ Value │ ├───────────────────────────────┼───────────────┼─────────┤ │tgamma(), tgammaf(), tgammal() │ Thread safety │ MTSafe │ └───────────────────────────────┴───────────────┴─────────┘
C99, POSIX.12001, POSIX.12008.
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).
Before version 2.18, the glibc implementation of these functions did not set errno to EDOM when x is negative infinity. 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.
gamma(3), lgamma(3)
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