tgammal(3)

1tgamma(3)                  Library Functions Manual                  tgamma(3)
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NAME

6       tgamma, tgammaf, tgammal - true gamma function
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LIBRARY

9       Math library (libm, -lm)
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SYNOPSIS

12       #include <math.h>
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14       double tgamma(double x);
15       float tgammaf(float x);
16       long double tgammal(long double x);
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18   Feature Test Macro Requirements for glibc (see feature_test_macros(7)):
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20       tgamma(), tgammaf(), tgammal():
21           _ISOC99_SOURCE || _POSIX_C_SOURCE >= 200112L
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DESCRIPTION

24       These functions calculate the Gamma function of x.
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26       The Gamma function is defined by
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28              Gamma(x) = integral from 0 to infinity of t^(x-1) e^-t dt
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30       It  is  defined  for every real number except for nonpositive integers.
31       For nonnegative integral m one has
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33              Gamma(m+1) = m!
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35       and, more generally, for all x:
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37              Gamma(x+1) = x * Gamma(x)
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39       Furthermore, the following is valid for all values  of  x  outside  the
40       poles:
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42              Gamma(x) * Gamma(1 - x) = PI / sin(PI * x)
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RETURN VALUE

45       On success, these functions return Gamma(x).
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47       If x is a NaN, a NaN is returned.
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49       If x is positive infinity, positive infinity is returned.
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51       If x is a negative integer, or is negative infinity, a domain error oc‐
52       curs, and a NaN is returned.
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54       If the result overflows, a range error occurs, and the functions return
55       HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the correct math‐
56       ematical sign.
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58       If the result underflows, a range error occurs, and the  functions  re‐
59       turn 0, with the correct mathematical sign.
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61       If  x  is  -0  or  +0,  a  pole  error occurs, and the functions return
62       HUGE_VAL, HUGE_VALF, or HUGE_VALL, respectively, with the same sign  as
63       the 0.
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ERRORS

66       See  math_error(7) for information on how to determine whether an error
67       has occurred when calling these functions.
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69       The following errors can occur:
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71       Domain error: x is a negative integer, or negative infinity
72              errno is set  to  EDOM.   An  invalid  floating-point  exception
73              (FE_INVALID) is raised (but see BUGS).
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75       Pole error: x is +0 or -0
76              errno  is set to ERANGE.  A divide-by-zero floating-point excep‐
77              tion (FE_DIVBYZERO) is raised.
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79       Range error: result overflow
80              errno is set to ERANGE.  An  overflow  floating-point  exception
81              (FE_OVERFLOW) is raised.
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83       glibc  also  gives the following error which is not specified in C99 or
84       POSIX.1-2001.
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86       Range error: result underflow
87              An underflow floating-point exception (FE_UNDERFLOW) is  raised,
88              and errno is set to ERANGE.
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ATTRIBUTES

91       For  an  explanation  of  the  terms  used  in  this  section,  see at‐
92       tributes(7).
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94       ┌────────────────────────────────────────────┬───────────────┬─────────┐
95       │Interface                                   │ Attribute     │ Value   │
96       ├────────────────────────────────────────────┼───────────────┼─────────┤
97       │tgamma(), tgammaf(), tgammal()              │ Thread safety │ MT-Safe │
98       └────────────────────────────────────────────┴───────────────┴─────────┘
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STANDARDS

101       C11, POSIX.1-2008.
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HISTORY

104       glibc 2.1.  C99, POSIX.1-2001.
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NOTES

107       This function had to be called "true gamma  function"  since  there  is
108       already  a  function gamma(3) that returns something else (see gamma(3)
109       for details).
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BUGS

112       Before glibc 2.18, the glibc implementation of these functions did  not
113       set errno to EDOM when x is negative infinity.
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115       Before  glibc 2.19, the glibc implementation of these functions did not
116       set errno to ERANGE on an underflow range error.
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118       In  glibc  versions  2.3.3  and  earlier,  an  argument  of  +0  or  -0
119       incorrectly  produced  a  domain  error  (errno  set  to  EDOM  and  an
120       FE_INVALID exception raised), rather than a pole error.
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