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

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DOI:

https://doi.org/10.26637/mjm204/005

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, Kampé de Fériet double Hypergeometric Function, Sri- vastava’s Triple Hypergeometric Function

Mathematics Subject Classification:

33B10, 33C05, 33C65
  • M. I. Qureshi Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India. https://orcid.org/0000-0002-5093-1925
  • C. W. Mohd Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India.
  • M. P. Chaudhary Former Researcher, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India. https://orcid.org/0000-0002-7329-2732
  • K. A. Quraishi Former Researcher, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India.
  • I. H. Khan Former Researcher, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India.
  • Pages: 373-391
  • Date Published: 01-10-2014
  • Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

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Published

01-10-2014

How to Cite

M. I. Qureshi, C. W. Mohd, M. P. Chaudhary, K. A. Quraishi, and I. H. Khan. “Analytical Solutions of Incomplete Elliptic Integrals Motivated by the Work of Ramanujan”. Malaya Journal of Matematik, vol. 2, no. 04, Oct. 2014, pp. 373-91, doi:10.26637/mjm204/005.

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Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

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