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

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

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

  1. 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   

  1. 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:

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:

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.

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