TRANSFORMATION FORMULAS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION WITH INTEGRAL PARAMETER DIFFERENCES

TRANSFORMATION FORMULAS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION WITH INTEGRAL PARAMETER DIFFERENCES

Transformation formulas of Euler and Kummertype 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...

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Veröffentlicht in:The Rocky Mountain journal of mathematics 2013-01, Vol.43 (1), p.291-327
Hauptverfasser: MILLER, A.R., PARIS, R.B.
Format: Artikel
Sprache:eng
Schlagworte:
33C15
33C20
Euler transformation
Generalized hypergeometric function
Kummer transformation
quadratic transformations
summation theorem
zeros of entire functions
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Zusammenfassung:Transformation formulas of Euler and Kummertype 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.
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-2013-43-1-291