Transformation formulas for the generalized hypergeometric function with integral parameter differences

A. R. Miller; Richard B. Paris

doi:10.1216/RMJ-2013-43-1-291

Transformation formulas for the generalized hypergeometric function with integral parameter differences

A. R. Miller, Richard B. Paris

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

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Abstract

Transformation formulas of Euler and Kummer-type are derived respectively for the generalized hypergeometric functions_r+2F_r+1(x) and _r+1F_r+1(x), where r pairs of numeratorial and denominatorial parameters differ by positive integers. Certain quadratic transformations for the former function, as well as a summation theorem when x = 1, are also considered.

Original language	English
Pages (from-to)	291-327
Number of pages	37
Journal	Rocky Mountain Journal of Mathematics
Volume	43
Issue number	1
DOIs	https://doi.org/10.1216/RMJ-2013-43-1-291
Publication status	Published - 2013

Keywords

Generalized hypergeometric function
Euler transformation
Kummer transformation
Quadratic transformations
Summation theorem
Zeros of entire functions

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10.1216/RMJ-2013-43-1-291

Paris_TransformationFormulasForTheGeneralizedHypergeometricFunction_Author_2013Accepted author manuscript, 390 KB

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abstract = "Transformation formulas of Euler and Kummer-type are derived respectively for the generalized hypergeometric functions r+2Fr+1(x) and r+1Fr+1(x), where r pairs of numeratorial and denominatorial parameters differ by positive integers. Certain quadratic transformations for the former function, as well as a summation theorem when x = 1, are also considered. ",

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AB - Transformation formulas of Euler and Kummer-type are derived respectively for the generalized hypergeometric functions r+2Fr+1(x) and r+1Fr+1(x), where r pairs of numeratorial and denominatorial parameters differ by positive integers. Certain quadratic transformations for the former function, as well as a summation theorem when x = 1, are also considered.

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DO - 10.1216/RMJ-2013-43-1-291

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JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

IS - 1

ER -

Transformation formulas for the generalized hypergeometric function with integral parameter differences

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