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32 .\" @(#)lgamma.3 8.2 (Berkeley) 12/11/93
41 .Nd log gamma function, gamma function
54 returns ln\||\(*G(x)| where
55 .Bd -unfilled -offset indent
56 \(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt for x > 0 and
58 \(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
62 returns ln\||\(*G(x)|.
66 returns the sign of \(*G(x).
69 returns \(*G(x), with no effect on
72 Do not use the expression
73 .Dq Li signgam\(**exp(lgamma(x))
74 to compute g := \(*G(x).
75 Instead use a program like this (in C):
76 .Bd -literal -offset indent
77 lg = lgamma(x); g = signgam\(**exp(lg);
82 has returned can signgam be correct.
84 For arguments in its range,
86 is preferred, as for positive arguments
87 it is accurate to within one unit in the last place.
90 will lose up to 10 significant bits.
95 return appropriate values unless an argument is out of range.
96 Overflow will occur for sufficiently large positive values, and
97 non-positive integers.
100 the reserved operator is returned,
105 For large non-integer negative values,
122 was originally dedicated to the
124 function, so some old code may no longer be compatible.