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The asymptotic expansion of a generalised incomplete gamma function
Journal of Computational and Applied Mathematics, 2003 The generalization has the form \(\Gamma_p(a,z)=\int_z^\infty t^{a-1} F_{2p}(t)\,dt\), where \(p=1,2,3,\ldots\) and \[ F_{2p}(t)=\sum_{k=0}^\infty (-1)^k {z^{k/p}\;\Gamma((2k+1)/(2p))\over k!\;\Gamma(k+1/2)}. \] Because \(F_2(t)=e^{-t}\), the function \(\Gamma_1(a,z)\) is the standard incomplete gamma function.
R B Paris
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Computation of the incomplete gamma function ratios and their inverse
ACM Transactions on Mathematical Software, 1986An algorithm is given for computing the incomplete gamma function ratios P ( a , x ) and Q> ( a , x ) for a ⪈ 0, x ⪈ 0, a +
Armido R. Didonato, Alfred H. Morris Jr.
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Products of incomplete gamma functions
Analysis, 2015AbstractMany properties of gamma functions are known. In this paper, we extend similar properties to incomplete gamma functions.
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The Incomplete Gamma Function Expressed as a Sum of Macdonald Functions
Results in Mathematics, 2001The author uses the expansion of the incomplete gamma function defined by \[ \gamma(\nu,z)=\sqrt{{2\over\pi}}\int_0^z s^{\nu-1/2} K_{1/2}(s) ds,\quad \Re \nu>0, \] in terms of the modified Bessel functions of the second kind \(K_{n+1/2}(z)\). This expansion allows to evaluate different types of integrals of interest in atomic physics.
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Incomplete Gamma and Error Functions: 10977
The American Mathematical Monthly, 2004Carl Axness +2 more
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