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Applications of hypergeometric summation theorems of kummer and dixon involving double series
Authors:HM SRIVASTAVA
Institution: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
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 reduction 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.
Keywords:Pochhammer's symbol  Gamma function  series identities  hypergeometric reduction formulas  Srivastava-Daoust double and multiple hypergeometric functions  Legendre's duplication formula  Gauss-Legendre multiplication formula  Kummer's theorem  Dixon's theorem
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