| DEFUN_DLD (gammainc, args,,"-*- texinfo -*-\n\
@deftypefn {Mapping Function} {} gammainc (@var{x}, @var{a})\n\
@deftypefnx {Mapping Function} {} gammainc (@var{x}, @var{a}, \"lower\")\n\
@deftypefnx {Mapping Function} {} gammainc (@var{x}, @var{a}, \"upper\")\n\
Compute the normalized incomplete gamma function,\n\
@tex\n\
$$\n\
\\gamma (x, a) = {1 \\over {\\Gamma (a)}}\\displaystyle{\\int_0^x t^{a-1} e^{-t} dt}\n\
$$\n\
@end tex\n\
@ifnottex\n\
\n\
@example\n\
@group\n\
x\n\
1 /\n\
gammainc (x, a) = --------- | exp (-t) t^(a-1) dt\n\
gamma (a) /\n\
t=0\n\
@end group\n\
@end example\n\
\n\
@end ifnottex\n\
with the limiting value of 1 as @var{x} approaches infinity.\n\
The standard notation is @math{P(a,x)}, e.g., Abramowitz and Stegun (6.5.1).\n\
\n\
If @var{a} is scalar, then @code{gammainc (@var{x}, @var{a})} is returned\n\
for each element of @var{x} and vice versa.\n\
\n\
If neither @var{x} nor @var{a} is scalar, the sizes of @var{x} and\n\
@var{a} must agree, and @code{gammainc} is applied element-by-element.\n\
\n\
By default the incomplete gamma function integrated from 0 to @var{x} is\n\
computed. If \"upper\" is given then the complementary function integrated\n\
from @var{x} to infinity is calculated. It should be noted that\n\
\n\
@example\n\
gammainc (@var{x}, @var{a}) @equiv{} 1 - gammainc (@var{x}, @var{a}, \"upper\")\n\
@end example\n\
@seealso{gamma, lgamma}\n\
@end deftypefn") |