An extension of Saalschütz's summation theorem for the series r+3Fr+2

Yong S. Kim; Arjun K. Rathie; Richard B. Paris

doi:10.1080/10652469.2013.777721

An extension of Saalschütz's summation theorem for the series _r+3F_r+2

Yong S. Kim, Arjun K. Rathie, Richard B. Paris

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

6 Citations (Scopus)

124 Downloads (Pure)

Abstract

The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series _r+3F_r+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear].

Original language	English
Pages (from-to)	916-921
Number of pages	6
Journal	Integral Transforms and Special Functions
Volume	24
Issue number	11
Early online date	16 May 2013
DOIs	https://doi.org/10.1080/10652469.2013.777721
Publication status	Published - 2013

Keywords

Generalized hypergeometric series
Unit argument
Saalschütz's theorem

Access to Document

10.1080/10652469.2013.777721

Paris_AnExtinsionOfSaalschutz'sSummation_Author_2013Accepted author manuscript, 309 KB

Cite this

@article{95ca3f4a4f93422c9278aa7fcaa6f5ba,

title = "An extension of Saalsch{\"u}tz's summation theorem for the series r+3Fr+2",

abstract = "The aim in this research note is to provide an extension of Saalsch{\"u}tz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear].",

author = "Kim, {Yong S.} and Rathie, {Arjun K.} and Paris, {Richard B.}",

year = "2013",

doi = "10.1080/10652469.2013.777721",

language = "English",

volume = "24",

pages = "916--921",

journal = "Integral Transforms and Special Functions",

issn = "1065-2469",

publisher = "Taylor and Francis Ltd.",

number = "11",

}

TY - JOUR

T1 - An extension of Saalschütz's summation theorem for the series r+3Fr+2

AU - Kim, Yong S.

AU - Rathie, Arjun K.

AU - Paris, Richard B.

PY - 2013

Y1 - 2013

N2 - The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear].

AB - The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is obtained by exploiting a generalization of an Euler-type transformation recently derived by Miller and Paris [Transformation formulas for the generalized hypergeometric function with integral parameter differences. Rocky Mountain J Math. 2013;43, to appear].

U2 - 10.1080/10652469.2013.777721

DO - 10.1080/10652469.2013.777721

M3 - Article

VL - 24

SP - 916

EP - 921

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

SN - 1065-2469

IS - 11

ER -