Multiplication and Translation Formulas for the Generalized Hypergeometric Functions and Their Applications

In his paper, the following multiplication and translation formulae of the generalized hypergeometric functions ... and ... are discussed for positive integers n, r, s, where MT (θ, x) = θxх or θ + x and the notation aR,bS are r, s-dimensional vector, respectively. Similarly, the multiplication and...

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Bibliographic Details
Published in:IAENG international journal of applied mathematics 2019-11, Vol.49 (4), p.1-11
Main Authors: Sun, Zhongfeng, Qin, Huizeng
Format: Article
Language:English
Subjects:
Hypergeometric functions
Mathematical analysis
Multiplication
Polynomials
Online Access:Get full text
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Summary:In his paper, the following multiplication and translation formulae of the generalized hypergeometric functions ... and ... are discussed for positive integers n, r, s, where MT (θ, x) = θxх or θ + x and the notation aR,bS are r, s-dimensional vector, respectively. Similarly, the multiplication and translation formulas for the basic hypergeometric seriesrφs can also be derived. Based on these results, the multiplication and translation formulas for the classical continuous, discrete orthogonal polynomials and the q-classical orthogonal polynomials which are associated withrFs orrφs can be established directly.
ISSN:1992-9978
1992-9986