Analytical solutions of incomplete elliptic integrals motivated by the work of Ramanujan

M. I. Qureshia, C. W. Mohdb, M. P. Chaudharyc,*, K. A. Quraishid and I. H. Khand

Analytical solutions of incomplete elliptic integrals motivated by the work of Ramanujan

Authors :

M. I. Qureshi^a, C. W. Mohd^b, M. P. Chaudhary^c,*, K. A. Quraishi^d and I. H. Khan^d

Author Address :

^a,bDepartment of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India.
^c,dFormer Researcher, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India.

*Corresponding author.

Abstract :

In this paper, we obtain exact solutions of some unsolved incomplete elliptic integrals of first, second and third kinds, given in Entry 7 of Chapter XVII of second notebook of Srinivasa Ramanujan. Furthermore, we generalize these elliptic integrals in the forms of multiple series identities involving bounded multiple sequences.

Keywords :

Gaussian Hypergeometric Function; Incomplete Elliptic Integrals; Multiple Series Identities; Srivastava-Daoust double Hypergeometric Function ; Kamp’{e} de F&rsqu

DOI :

Article Info :

Received : March 14, 2014; Accepted : August 23, 2014.