Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions

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dc.citation.epage434en_US
dc.citation.issueNumber1en_US
dc.citation.spage420en_US
dc.citation.volumeNumber388en_US
dc.contributor.authorYesilyurt, H.en_US
dc.date.accessioned2016-02-08T09:47:21Z
dc.date.available2016-02-08T09:47:21Z
dc.date.issued2012en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractIn 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.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T09:47:21Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2012en
dc.identifier.doi10.1016/j.jmaa.2011.11.004en_US
dc.identifier.eissn1096-0813
dc.identifier.issn0022-247X
dc.identifier.urihttp://hdl.handle.net/11693/21510
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.jmaa.2011.11.004en_US
dc.source.titleJournal of Mathematical Analysis and Applicationsen_US
dc.subjectTheta functionsen_US
dc.subjectModular equationsen_US
dc.subjectRogers–Ramanujan functionsen_US
dc.titleElementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functionsen_US
dc.typeArticleen_US

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