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

Print ISSN: 0972-7752

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 fi rst kind, involving theta-functions, which are analogous to integrals recorded by Ramanujan in his Lost Notebook.

Keywords and Phrases

Dedekind eta-function, Theta-functions, Eisenstein series, Bilateral basic hypergeometric series, Incomplete elliptic integrals.

A.M.S. subject classification

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

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