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    Command:

    tgamma

    
    
    

    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 ||
               _POSIX_C_SOURCE >= 200112L;
               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 math-
           ematical sign.
    
           If  the  result  underflows,  a  range  error occurs, and the functions
           return 0, with the correct mathematical sign.
    
           Pole error: x is +0 or -0
                  errno 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.
    
    
    

    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 incor-
           rectly 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)
    
    
    

    GNU 2010-09-20 TGAMMA(3)

    
    
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