y = gamma(a)
y = gammainc(x,a)
y = gammaln(a)
y = gamma(a)
returns the gamma function evaluated at the elements of a
. The gamma function is defined by the integral:
The gamma function interpolates the factorial function. For integer n
gamma(n+1) = n! = prod(1:n)
y = gammainc(x,a)
returns the incomplete gamma function defined by
y = gammaln(a)
returns the logarithm of the gamma function,
gammaln(a) = log(gamma(a))
gammaln
avoids the underflow and overflow that may occur if it is computed directly using log(gamma(a))
.
gamma
and gammaln
are based on algorithms outlined in [1]. Several different minimax rational approximations are used depending upon the value of a
. Computation of the incomplete gamma function is based on the algorithm in [2].
[2] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965, sec. 6.5.
(c) Copyright 1994 by The MathWorks, Inc.