tgamma(3) Library Functions Manual tgamma(3) NAME tgamma, tgammaf, tgammal - true gamma function LIBRARY Math library (libm, -lm) SYNOPSIS #include <math.h> double tgamma(double x); float tgammaf(float x); long double tgammal(long double x); 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 oc- curs, 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 math- ematical sign. If the result underflows, a range error occurs, and the functions re- turn 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 excep- tion (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 were added in glibc 2.1. ATTRIBUTES For an explanation of the terms used in this section, see at- tributes(7). ┌────────────────────────────────────────────┬───────────────┬─────────┐ │Interface │ Attribute │ Value │ ├────────────────────────────────────────────┼───────────────┼─────────┤ │tgamma(), tgammaf(), tgammal() │ Thread safety │ MT-Safe │ └────────────────────────────────────────────┴───────────────┴─────────┘ STANDARDS C99, POSIX.1-2001, POSIX.1-2008. NOTES This function had to be called "true gamma function" since there is al- ready a function gamma(3) that returns something else (see gamma(3) for details). BUGS Before glibc 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 incorrect- ly produced a domain error (errno set to EDOM and an FE_INVALID excep- tion raised), rather than a pole error. SEE ALSO gamma(3), lgamma(3) Linux man-pages 6.03 2023-02-10 tgamma(3)
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