RAMANUJAN'S EISENSTEIN SERIES OF LEVEL 3 AND 6, ITS APPLICATION

K. R. Vasuki; R. G. Veeresha; E. N. Bhuvan

K. R. Vasuki Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru - 570 006, INDIA.

R. G. Veeresha Department of Mathematics Sri Jayachamarajendra College of Engineering Manasagangotri, Mysuru - 570 006, INDIA.

E. N. Bhuvan Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru - 570 006, INDIA.

Volume 14, Issue 1 Pages 01-18 April 30, 2018 185 downloads

Article overview

Abstract

In this paper, we give an elementary proof of Eisenstein series of level 3 and 6, recorded by Ramanujan. Further, as an application of these Eisenstein series identities, we establish certain incomplete elliptic integrals of the first kind, involving theta-functions, which are analogous to integrals recorded by Ramanujan in his Lost Notebook.

Keywords and Phrases

Dedekind eta-functionTheta-functionsEisenstein seriesBilateral basic hypergeometric seriesIncomplete elliptic integrals.

AMS Subject Classification

11F11, 11F20, 11M36, 33D15, 33E05.

Reference information

How to Cite

K. R. Vasuki, R. G. Veeresha, E. N. Bhuvan (2018). RAMANUJAN'S EISENSTEIN SERIES OF LEVEL 3 AND 6, ITS APPLICATION. South East Asian Journal of Mathematics and Mathematical Sciences, 14(1), 01-18.

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