On certain generalized incomplete gamma functions
type: Item
instance of: scholarly article
title: On certain generalized incomplete gamma functions
zbMATH Open document ID: 0933.33003
DOI: 10.1016/S0377-0427(98)00031-4
author: Allen Richard Miller
author: Ira S. Moskowitz
published in: Journal of Computational and Applied Mathematics
publication date: 1999-08-22T00:00:00Z
review text: \textit{M. A. Chaudhry} and \textit{S. M. Zubair} [J. Comput. Appl. Math. 55, No. 1, 99-124 (1994; Zbl 0833.33002)] have introduced a generalized incomplete gamma function \(\Gamma(\nu,x; z)\) which reduces to the incomplete gamma function when its variable \(z\) vanishes. In this paper, the authors show that \(\Gamma(\nu, x;z)\) may be written essentially as a single Kampé de Fériet function which in turn may be expressed as a linear combination of two incomplete Weber integrals. Then by using the properties of the latter integrals additional representations for \(\Gamma(\nu,x; z)\) are deduced. In particular, it is shown that \(\Gamma(\nu, x;z)\) can be completely determined by a number of modified Bessel functions for all \(\nu\neq 0\) provided the values of the two incomplete Weber integrals are known for \(0< \text{Re }\nu\leq 1\). When \(\nu= 0\), connections between the generalized incomplete gamma function and incomplete Lipschitz-Hankel integrals are derived and existence of such connections with other special functions are indicated.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 33B20
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33C70
zbMATH DE Number: 1326403
zbMATH Keywords: Bessel functions
zbMATH Keywords: generalized incomplete gamma function
zbMATH Keywords: Kampé de Fériet function
zbMATH Keywords: incomplete Lipschitz-Hankel integrals
Wikidata QID: Q56271101
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1326403