Comments on "new hypergeometric identities arising from gauss's second summation theorem"

Medhat K. Rakha, Arjun K. Rathie, Purnima Chopra, Richard B. Paris

Research output: Contribution to journalArticle

Abstract

In 1997, Exton [J. Comput. Appl. Math. 88 (1997) 269-274] obtained a general transformation involving hypergeometric functions by elementary manipulation of series. A number of hypergeometric identities that had not been previously recorded in the literature were then deduced by application of Gauss' second summation theorem and other known hypergeometric summation theorems. However, some of the results stated by Exton contain errors. It is the purpose of this note to present the corrected forms of these hypergeometric identities. 2000 Mathematics Subject Classification: 33C20; 68Q40.

Original languageEnglish
Pages (from-to)87-89
Number of pages3
JournalMiskolc Mathematical Notes
Volume13
Issue number1
Publication statusPublished - 2012

Fingerprint

Summation
Gauss
Theorem
Hypergeometric Functions
Manipulation
Series
Form

Keywords

  • Generalized hypergeometric series
  • Hypergeometric identities

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Control and Optimization
  • Discrete Mathematics and Combinatorics
  • Numerical Analysis

Cite this

Comments on "new hypergeometric identities arising from gauss's second summation theorem". / Rakha, Medhat K.; Rathie, Arjun K.; Chopra, Purnima; Paris, Richard B.

In: Miskolc Mathematical Notes, Vol. 13, No. 1, 2012, p. 87-89.

Research output: Contribution to journalArticle

Rakha, Medhat K. ; Rathie, Arjun K. ; Chopra, Purnima ; Paris, Richard B. / Comments on "new hypergeometric identities arising from gauss's second summation theorem". In: Miskolc Mathematical Notes. 2012 ; Vol. 13, No. 1. pp. 87-89.
@article{c53c56f8489240bba86a4986f71709a2,
title = "Comments on {"}new hypergeometric identities arising from gauss's second summation theorem{"}",
abstract = "In 1997, Exton [J. Comput. Appl. Math. 88 (1997) 269-274] obtained a general transformation involving hypergeometric functions by elementary manipulation of series. A number of hypergeometric identities that had not been previously recorded in the literature were then deduced by application of Gauss' second summation theorem and other known hypergeometric summation theorems. However, some of the results stated by Exton contain errors. It is the purpose of this note to present the corrected forms of these hypergeometric identities. 2000 Mathematics Subject Classification: 33C20; 68Q40.",
keywords = "Generalized hypergeometric series, Hypergeometric identities",
author = "Rakha, {Medhat K.} and Rathie, {Arjun K.} and Purnima Chopra and Paris, {Richard B.}",
year = "2012",
language = "English",
volume = "13",
pages = "87--89",
journal = "Miskolc Mathematical Notes",
issn = "1787-2405",
publisher = "Miskolc University Press",
number = "1",

}

TY - JOUR

T1 - Comments on "new hypergeometric identities arising from gauss's second summation theorem"

AU - Rakha, Medhat K.

AU - Rathie, Arjun K.

AU - Chopra, Purnima

AU - Paris, Richard B.

PY - 2012

Y1 - 2012

N2 - In 1997, Exton [J. Comput. Appl. Math. 88 (1997) 269-274] obtained a general transformation involving hypergeometric functions by elementary manipulation of series. A number of hypergeometric identities that had not been previously recorded in the literature were then deduced by application of Gauss' second summation theorem and other known hypergeometric summation theorems. However, some of the results stated by Exton contain errors. It is the purpose of this note to present the corrected forms of these hypergeometric identities. 2000 Mathematics Subject Classification: 33C20; 68Q40.

AB - In 1997, Exton [J. Comput. Appl. Math. 88 (1997) 269-274] obtained a general transformation involving hypergeometric functions by elementary manipulation of series. A number of hypergeometric identities that had not been previously recorded in the literature were then deduced by application of Gauss' second summation theorem and other known hypergeometric summation theorems. However, some of the results stated by Exton contain errors. It is the purpose of this note to present the corrected forms of these hypergeometric identities. 2000 Mathematics Subject Classification: 33C20; 68Q40.

KW - Generalized hypergeometric series

KW - Hypergeometric identities

UR - http://www.scopus.com/inward/record.url?scp=84868096185&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868096185&partnerID=8YFLogxK

M3 - Article

VL - 13

SP - 87

EP - 89

JO - Miskolc Mathematical Notes

JF - Miskolc Mathematical Notes

SN - 1787-2405

IS - 1

ER -