Manpage of TGAMMA
TGAMMASection: Linux Programmer's Manual (3)
NAMEtgamma, tgammaf, tgammal - true gamma function
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
DESCRIPTIONThese 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 mone 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 xoutside the poles:
- Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
RETURN VALUEOn success, these functions return Gamma(x).
If xis a NaN, a NaN is returned.
If xis positive infinity, positive infinity is returned.
If xis 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.
ERRORSSee 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
- errnois set to EDOM. An invalid floating-point exception (FE_INVALID) is raised (but see BUGS).
- Pole error: x is +0 or -0
- errnois set to ERANGE. A divide-by-zero floating-point exception (FE_DIVBYZERO) is raised.
- Range error: result overflow
- errnois 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 errnois set to ERANGE.
VERSIONSThese functions first appeared in glibc in version 2.1.
ATTRIBUTESFor an explanation of the terms used in this section, see attributes(7).
|tgamma(), tgammaf(), tgammal()||Thread safety||MT-Safe|
CONFORMING TOC99, POSIX.1-2001, POSIX.1-2008.
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).
BUGSBefore version 2.18, the glibc implementation of these functions did not set errnoto EDOMwhen xis negative infinity.
Before glibc 2.19, the glibc implementation of these functions did not set errnoto ERANGEon an underflow range error. x
SEE ALSOgamma(3), lgamma(3)
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