TGAMMA(3)                                           Linux Programmer's Manual                                          TGAMMA(3)



NAME
       tgamma, tgammaf, tgammal - true gamma function

SYNOPSIS
       #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(): _XOPEN_SOURCE >= 600 || _ISOC99_SOURCE; or cc -std=c99

DESCRIPTION
       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 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.

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 exception (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.

VERSIONS
       These functions first appeared in glibc in version 2.1.

CONFORMING TO
       C99, POSIX.1-2001.

NOTES
       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).

BUGS
       If 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 or -0 incorrectly produced a domain error (errno set to  EDOM  and
       an FE_INVALID exception raised), rather than a pole error.

SEE ALSO
       gamma(3), lgamma(3)

COLOPHON
       This  page  is  part of release 3.25 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/.



GNU                                                        2008-08-11                                                  TGAMMA(3)