Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x)

A. R. Miller, Richard B. Paris

Research output: Contribution to journalArticle

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Abstract

We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for r+1 F r+1 (x) that was recently derived in a different way.
Original languageEnglish
Pages (from-to)31–45
Number of pages15
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume62
Issue number1
DOIs
StatePublished - Feb 2011

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Generalized hypergeometric function
Transformation formula
Euler
hypergeometric functions
Gauss hypergeometric function
Deduce
unity

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Miller, A. R.; Paris, Richard B. / Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x).

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 62, No. 1, 02.2011, p. 31–45.

Research output: Contribution to journalArticle

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Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x). / Miller, A. R.; Paris, Richard B.

In: Zeitschrift fur Angewandte Mathematik und Physik, Vol. 62, No. 1, 02.2011, p. 31–45.

Research output: Contribution to journalArticle

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AB - We provide generalizations of two of Euler’s classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function r+2 F r+1(x) when there are additional numeratorial and denominatorial parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for r+1 F r+1 (x) that was recently derived in a different way.

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