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, and errno is set to ERANGE.
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. Before glibc 2.19, the glibc implementation of these functions did not set errno to ERANGE on an underflow range error. 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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Pages that refer to this page: gamma(3), lgamma(3)
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