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

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

12 Citations (Scopus)

89 Downloads (Pure)

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

Access to Document

10.1007/s00033-010-0085-0

ParisZAMPAuthor2011Accepted author manuscript, 161 KB

Fingerprint Dive into the research topics of 'Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x)'. Together they form a unique fingerprint.

Cite this

@article{30e4ad50271e40a7bfb3dc6515871b50,

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

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.",

author = "Miller, {A. R.} and Paris, {Richard B.}",

year = "2011",

month = feb,

doi = "10.1007/s00033-010-0085-0",

language = "English",

volume = "62",

pages = "31–45",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "1",

}

TY - JOUR

T1 - Euler-type transformations for the generalized hypergeometric function r+2Fr+1(x)

AU - Miller, A. R.

AU - Paris, Richard B.

PY - 2011/2

Y1 - 2011/2

N2 - 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.

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.

U2 - 10.1007/s00033-010-0085-0

DO - 10.1007/s00033-010-0085-0

M3 - Article

VL - 62

SP - 31

EP - 45

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 1

ER -