A generalization of a modular identity of Rogers
Author
Yeşilyurt, Hamza
Date
2009Source Title
Journal of Number Theory
Print ISSN
0022-314X
Publisher
Academic Press
Volume
129
Issue
6
Pages
1256 - 1271
Language
English
Type
ArticleItem Usage Stats
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Abstract
In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. Most of the elementary proofs given for these identities are based on Schröter-type theta function identities in particular, the identities of L.J. Rogers. We give a generalization of Rogers's identity that also generalizes similar formulas of H. Schröter, and of R. Blecksmith, J. Brillhart, and I. Gerst. Applications to modular equations, Ramanujan's identities for the Rogers-Ramanujan functions as well as new identities for these functions are given.