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 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, and errno is set to
              ERANGE.

ATTRIBUTES

       For an explanation of the terms used in this section, see attributes(7).

       ┌───────────────────────────────────────────────────────────────┬───────────────┬─────────┐
       │Interface                                                      │ Attribute     │ Value   │
       ├───────────────────────────────────────────────────────────────┼───────────────┼─────────┤
       │tgamma(), tgammaf(), tgammal()                                 │ Thread safety │ MT-Safe │
       └───────────────────────────────────────────────────────────────┴───────────────┴─────────┘

STANDARDS

       C11, POSIX.1-2008.

HISTORY

       glibc 2.1.  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

       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 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)