tgamma(3) — Linux manual page

tgamma(3)               Library Functions Manual               tgamma(3)

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)

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Linux man-pages 6.9.1          2024-05-02                      tgamma(3)

Pages that refer to this page: gamma(3), lgamma(3)

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