Transformation formulas for the generalized hypergeometric function with integral parameter differences

A. R. Miller, Richard B. Paris

Research output: Contribution to journal › Article

17 Citations (Scopus)
519 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)291-327
Number of pages37
JournalRocky Mountain Journal of Mathematics
Volume43
Issue number1
DOIs
Publication statusPublished - 2013

Fingerprint

Generalized Hypergeometric Function
Transformation Formula
Summation
Euler
Integer
Theorem

Cite this

Miller, A. R. ; Paris, Richard B. / Transformation formulas for the generalized hypergeometric function with integral parameter differences. In: Rocky Mountain Journal of Mathematics. 2013 ; Vol. 43, No. 1. pp. 291-327.
@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",

}

Miller, AR & Paris, RB 2013, 'Transformation formulas for the generalized hypergeometric function with integral parameter differences', Rocky Mountain Journal of Mathematics, vol. 43, no. 1, pp. 291-327. https://doi.org/10.1216/RMJ-2013-43-1-291

Transformation formulas for the generalized hypergeometric function with integral parameter differences. / Miller, A. R.; Paris, Richard B.

In: Rocky Mountain Journal of Mathematics, Vol. 43, No. 1, 2013, p. 291-327.

Research output: Contribution to journal › Article

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 -

Miller AR, Paris RB. Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain Journal of Mathematics. 2013;43(1):291-327. https://doi.org/10.1216/RMJ-2013-43-1-291

Access to Document