Some classes of generating functions associated with a certain family of extended and generalized hypergeometric functions

Recently, Srivastava et al. (2012) [11] introduced and initiated the study of many interesting fundamental properties and characteristics of a certain pair of potentially useful families of the so-called generalized incomplete hypergeometric functions. Ever since then there have appeared many closel...

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Published in:Applied mathematics and computation Vol. 243; pp. 132 - 137
Main Author: Srivastava, Rekha
Format: Journal Article
Language:English
Published: Elsevier Inc 15.09.2014
Subjects:
Computation
Dealing
Gamma and extended gamma functions
Gauss hypergeometric function
Generalized and extended hypergeometric functions and polynomials
Hypergeometric functions
Linear, bilinear and bilateral (or mixed multilateral) generating functions
Mathematical analysis
Mathematical models
Multilateral
Pochhammer’s symbol and its extended version
Polynomials
Symbols
Gamma and extended gamma functions
Gauss hypergeometric function
Generalized and extended hypergeometric functions and polynomials
Pochhammer’s symbol and its extended version
Linear, bilinear and bilateral (or mixed multilateral) generating functions
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:Recently, Srivastava et al. (2012) [11] introduced and initiated the study of many interesting fundamental properties and characteristics of a certain pair of potentially useful families of the so-called generalized incomplete hypergeometric functions. Ever since then there have appeared many closely-related works dealing essentially with notable developments involving various classes of generalized hypergeometric functions and generalized hypergeometric polynomials, which are defined by means of the corresponding incomplete and other novel extensions of the familiar Pochhammer symbol. Here, in this sequel to some of these earlier works, we first derive two remarkably distinct classes of hypergeometric generating functions and then apply each of them in deducing a family of linear, bilinear and bilateral (or mixed multilateral) generating functions. We also consider various (known or new) special cases and consequences of the results presented in this paper.
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ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2014.05.074