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

A. R. Miller; Richard B. Paris

doi:10.1007/s00033-010-0085-0

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

A. R. Miller, Richard B. Paris

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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 language	English
Pages (from-to)	31–45
Number of pages	15
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/s00033-010-0085-0
Publication status	Published - Feb 2011

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abstract = "We provide generalizations of two of Euler{\textquoteright}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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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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DO - 10.1007/s00033-010-0085-0

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JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

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