1TGAMMA(3)                     libc math functions                    TGAMMA(3)
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NAME

6       tgamma, tgammaf, tgammal - true gamma function
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SYNOPSIS

9       #include <math.h>
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11       double tgamma(double x);
12       float tgammaf(float x);
13       long double tgammal(long double x);
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15       Compile with -std=c99; link with -lm.
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DESCRIPTION

18       The Gamma function is defined by
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20        Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
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22       It  is  defined for every real number except for non-positive integers.
23       For nonnegative integral m one has
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25        Gamma(m+1) = m!
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27       and, more generally, for all x:
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29        Gamma(x+1) = x * Gamma(x)
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31       Furthermore, the following is valid for all values  of  x  outside  the
32       poles:
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34        Gamma(x) * Gamma(1-x) = PI/sin(PI*x)
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36       This  function returns the value of the Gamma function for the argument
37       x. It had to be called "true gamma function" since there is  already  a
38       function gamma() that returns something else.
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ERRORS

41       In  order  to  check  for errors, set errno to zero and call feclearex‐
42       cept(FE_ALL_EXCEPT) before calling these functions. On return, if errno
43       is  non-zero  or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW |
44       FE_UNDERFLOW) is non-zero, an error has occurred.
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46       A range error occurs if x is too large.  A pole error occurs  if  x  is
47       zero.  A domain error (or a pole error) occurs if x is a negative inte‐
48       ger.
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CONFORMING TO

51       C99.
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SEE ALSO

54       gamma(3), lgamma(3)
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58GNU                               2004-11-15                         TGAMMA(3)