On a result related to transformations and summations of generalized hypergeometric series

A. R. Miller, Richard B. Paris

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We deduce an explicit representation for the coefficients in a finite expansion of a certain class of generalized hypergeometric functions that contain multiple pairs of numeratorial and denominatorial parameters differing by positive integers. The expansion alluded to is given in terms of these coefficients and hypergeometric functions of lower order. Applications to Euler and Kummer-type transformations of a subclass of the generalized hypergeometric functions mentioned above together with an extension of the Karlsson-Minton summation formula are provided.
Original languageEnglish
Pages (from-to)205-210
Number of pages6
JournalMathematical Communications
Volume17
Issue number1
Publication statusPublished - 2012

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Generalized Hypergeometric Series
Generalized Hypergeometric Function
Summation
Summation Formula
Hypergeometric Functions
Coefficient
Euler
Deduce
Integer

Cite this

Miller, A. R. ; Paris, Richard B. / On a result related to transformations and summations of generalized hypergeometric series. In: Mathematical Communications. 2012 ; Vol. 17, No. 1. pp. 205-210.
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On a result related to transformations and summations of generalized hypergeometric series. / Miller, A. R.; Paris, Richard B.

In: Mathematical Communications, Vol. 17, No. 1, 2012, p. 205-210.

Research output: Contribution to journalArticle

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AB - We deduce an explicit representation for the coefficients in a finite expansion of a certain class of generalized hypergeometric functions that contain multiple pairs of numeratorial and denominatorial parameters differing by positive integers. The expansion alluded to is given in terms of these coefficients and hypergeometric functions of lower order. Applications to Euler and Kummer-type transformations of a subclass of the generalized hypergeometric functions mentioned above together with an extension of the Karlsson-Minton summation formula are provided.

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