Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions
Date
2012
Authors
Yesilyurt, H.
Advisor
Instructor
Source Title
Journal of Mathematical Analysis and Applications
Print ISSN
0022-247X
Electronic ISSN
1096-0813
Publisher
Elsevier
Volume
388
Issue
1
Pages
420 - 434
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract
In a handwritten manuscript published with his lost notebook, Ramanujan stated without proofs forty identities for the Rogers-Ramanujan functions. With one exception all of Ramanujan's identities were proved. In this paper, we provide a proof for the remaining identity together with new elementary proofs for two identities of Ramanujan which were previously proved using the theory of modular forms. Ramanujan stated that each of his formula was the simplest of a large class. Our proofs are constructive and permit us to obtain several analogous identities which could have been stated by Ramanujan and may very well belong to his large class of identities. © 2011 Elsevier Inc.
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Keywords
Theta functions, Modular equations, Rogers–Ramanujan functions