APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

doi:10.1016/S0252-9602(14)60034-5

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 619-628.doi: 10.1016/S0252-9602(14)60034-5

APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

H. M. SRIVASTAVA*|M. I. QURESHI|Kaleem A. QURAISHI|Ashish ARORA

Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada； Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi 110025, India； Section of Mathematics, Mewat Engineering College (Wakf), Palla, Nuh, Mewat 122107, Haryana, India； Department of Mathematics, Noida Institute of Engineering and Technology, Greater Noida, Gautambuddha Nagar 201306, Uttar Pradesh, India

收稿日期:2012-05-28 出版日期:2014-05-20 发布日期:2014-05-20
通讯作者: H. M. SRIVASTAVA，harimsri@math.uvic.ca E-mail:harimsri@math.uvic.ca；miqureshi delhi@yahoo.co.in；kaleemspn@yahoo.co.in；dr.ashisharora5@gmail.com

APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

H. M. SRIVASTAVA*|M. I. QURESHI|Kaleem A. QURAISHI|Ashish ARORA

Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada； Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi 110025, India； Section of Mathematics, Mewat Engineering College (Wakf), Palla, Nuh, Mewat 122107, Haryana, India； Department of Mathematics, Noida Institute of Engineering and Technology, Greater Noida, Gautambuddha Nagar 201306, Uttar Pradesh, India

Received:2012-05-28 Online:2014-05-20 Published:2014-05-20
Contact: H. M. SRIVASTAVA，harimsri@math.uvic.ca E-mail:harimsri@math.uvic.ca；miqureshi delhi@yahoo.co.in；kaleemspn@yahoo.co.in；dr.ashisharora5@gmail.com

摘要/Abstract

摘要：

Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduc-tion formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.

关键词: Pochhammer´s symbol, Gamma function, series identities, hypergeometric re-duction formulas, Srivastava-Daoust double and multiple hypergeometric func-tions, Legendre´s duplication formula, Gauss-Legendre multiplication formula,
Kummer´s theorem, Dixon´s theorem

Abstract:

Key words: Pochhammer´s symbol, Gamma function, series identities, hypergeometric re-duction formulas, Srivastava-Daoust double and multiple hypergeometric func-tions, Legendre´s duplication formula, Gauss-Legendre multiplication formula,
Kummer´s theorem, Dixon´s theorem

中图分类号:

33C20

H. M. SRIVASTAVA, M. I. QURESHI, Kaleem A. QURAISHI, Ashish ARORA. APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES[J]. 数学物理学报(英文版), 2014, 34(3): 619-628.

H. M. SRIVASTAVA, M. I. QURESHI, Kaleem A. QURAISHI, Ashish ARORA. APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES[J]. Acta mathematica scientia,Series B, 2014, 34(3): 619-628.

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APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

APPLICATIONS OF HYPERGEOMETRIC SUMMATION THEOREMS OF KUMMER AND DIXON INVOLVING DOUBLE SERIES

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