plucky (3) tgamma.3.gz

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)