Unification and Generalization of Two Product Theorems of Srinivasa Ramanujan Associated with Quadruple Hypergeometric Functions

Authors

Mohammad Idris Qureshi, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi-110025, India.Follow
Mohd Shadab, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi-110025, India.Follow

Author Country (or Countries)

India.

Abstract

The object of the present paper is to show that Ramanujan’s two reduction formulas [Entries 24 and 22 in chapter 13 of Ramanujan’s first notebook,see also Entries 18 and 16 in chapter 11 of Ramanujan’s second notebook] for the products of two hypergeometric functions, can be unified and generalized for general quadruple Gaussian hypergeometric functions of Srivastava, Pathan and Saigo, using series rearrangement technique.Using the theory of bounded multiple sequences, further generalizations of two product theorems of Srinivasa Ramanujan, are also given.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110430

Recommended Citation

Idris Qureshi, Mohammad and Shadab, Mohd (2017) "Unification and Generalization of Two Product Theorems of Srinivasa Ramanujan Associated with Quadruple Hypergeometric Functions," Applied Mathematics & Information Sciences: Vol. 11: Iss. 4, Article 30.
DOI: http://dx.doi.org/10.18576/amis/110430
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss4/30