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On conjectures of Koike and Somos for modular identities for the Rogers–Ramanujan functions

Department of Mathematics, Georgia Southwestern State University, 800 GSW State University Drive, Americus, GA 31709, USA

E-mail Address: Chadwick.Gugg@gsw.edu

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https://doi.org/10.1142/S1793042120400138Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue I: In Honor of Bruce Berndt’s 80th Birthday
Editors: George E. Andrews, Michael Filaseta and Ae Ja Yee

Abstract

In this paper, we prove modular identities conjectured by Koike and Somos for the Rogers–Ramanujan functions. Our methods focus on approaches that Ramanujan could have employed, including the theory of modular equations, dissections of identities, and methods derived from the approaches of Watson and Rogers.

Keywords:

AMSC: 11P84, 33D90

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