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

26 Citations (Scopus)

891 Downloads (Pure)

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

Access to Document

10.1216/RMJ-2013-43-1-291

Paris_TransformationFormulasForTheGeneralizedHypergeometricFunction_Author_2013Accepted author manuscript, 390 KB

Cite this

@article{7e8ddcf4628b4257beb4b9fb278e4503,

title = "Transformation formulas for the generalized hypergeometric function with integral parameter differences",

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.",

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

year = "2013",

doi = "10.1216/RMJ-2013-43-1-291",

language = "English",

volume = "43",

pages = "291--327",

journal = "Rocky Mountain Journal of Mathematics",

issn = "0035-7596",

publisher = "Rocky Mountain Mathematics Consortium",

number = "1",

}

TY - JOUR

T1 - Transformation formulas for the generalized hypergeometric function with integral parameter differences

AU - Miller, A. R.

AU - Paris, Richard B.

PY - 2013

Y1 - 2013

N2 - 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.

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.

U2 - 10.1216/RMJ-2013-43-1-291

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

M3 - Article

VL - 43

SP - 291

EP - 327

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

IS - 1

ER -

Transformation formulas for the generalized hypergeometric function with integral parameter differences

Abstract

Keywords

Access to Document

Fingerprint

Cite this