gamma function


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Related to gamma function: Incomplete gamma function

gamma function

n
(Mathematics) maths a function defined by Γ(x) = ∫0tx1etdt, where x is real and greater than zero
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where [[GAMMA].sub.r](s, ([[omega].sub.1], ..., [[omega].sub.r])) is the regularized version of the multiple gamma function introduced by Barnes [1].
using the symmetry formula [13] for the Gamma function in (17a).
where [mathematical expression not reproducible] is the lower incomplete gamma function. The survival function is
where: g(x, = dG(x, [xi]) with [xi] a parametric vector, [mathematical expression not reproducible] is the gamma function and [mathematical expression not reproducible] denotes the lower incomplete gamma function.
where [GAMMA](*) denotes the gamma function. The function [w.sub.v,b,c] unifies the Bessel, modified Bessel, and spherical Bessel functions.
Here and in what follows r denotes the gamma function. We also appeal to the common convention that if t+1-v is a pole of the gamma function and t + 1 is not a pole, then [t.sup.[v.bar.] = 0.
It is worth notable that the second-equality of (33) is used for incomplete Gamma function.
Taylor series for the reciprocal gamma function and multiple zeta values.
where [G.sup.m,n.sub.p,q] (x) is the Meijers G-function defined in [18], [GAMMA](x) denotes special Gamma function [18], p and q are positive integer numbers that satisfy p/q = [[gamma].sub.1]/[[gamma].sub.2], and [DELTA](j; x) [??] x/j, ..., (x + j - 1)/j.
provided the right hand-side is point-wise defined on [0, [infinity]), where [GAMMA](*) is the gamma function, which is defined by [GAMMA](q) = [[integral].sup.[infinity].sub.0] [t.sp.q-1] [e.sup.-t]dt.
where [gamma](a, x) stands for the incomplete Gamma function [12, Equation 8.443].