TGAMMA(3) Linux Programmer's Manual TGAMMA(3)[top]NAMEtgamma, tgammaf, tgammal - true gamma functionSYNOPSIS#include <math.h> double tgamma(double x); float tgammaf(float x); long double tgammal(long double x); Link withFeature Test Macro Requirements for glibc (see feature_test_macros(7)): tgamma(), tgammaf(), tgammal(): _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L; or cc -std=c99-lm.DESCRIPTIONThe 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 VALUEOn 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 math‐ ematical sign. If the result underflows, a range error occurs, and the functions return 0, with the correct mathematical sign. If x isor +0, a pole error occurs, and the functions return HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign as the 0.-0ERRORSSee 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 orerrno 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. errno is not set for this case.-0VERSIONSThese functions first appeared in glibc in version 2.1.CONFORMING TOC99, POSIX.1-2001.NOTESThis 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).BUGSIf x is negative infinity, errno is not set (it should be set to EDOM). In glibc versions 2.3.3 and earlier, an argument of +0 orincor‐ rectly produced a domain error (errno set to EDOM and an FE_INVALID exception raised), rather than a pole error.-0SEE ALSOgamma(3), lgamma(3)COLOPHONThis page is part of release 3.65 of the Linux man-pages project. A description of the project, and information about reporting bugs, can be found at http://www.kernel.org/doc/man-pages/.GNU2010-09-20 TGAMMA(3)

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