Incomplete gamma functions for large values of their variables

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Abstract

We consider the incomplete gamma functions Γ (a, z) and γ (a, z) for large values of their variables a and z. We derive four complementary asymptotic expansions which approximate these functions for large a and z with Arg (a) ≤ π and Arg (z) < π. Three of these expansions are given in terms of decreasing powers of a - z and are not valid near the transition point a = z. A fourth expansion is given in terms of decreasing powers of a and error functions and is valid for a near z. These expansions have a simpler structure than other expansions previously given in the literature. © 2004 Elsevier Inc. All rights reserved.

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Ferreira, C., López, J. L., & Pérez Sinusía, E. (2005). Incomplete gamma functions for large values of their variables. Advances in Applied Mathematics, 34(3), 467–485. https://doi.org/10.1016/j.aam.2004.08.001

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