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      A generalization of a modular identity of Rogers

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      Author
      Yeşilyurt, Hamza
      Date
      2009
      Source Title
      Journal of Number Theory
      Print ISSN
      0022-314X
      Publisher
      Academic Press
      Volume
      129
      Issue
      6
      Pages
      1256 - 1271
      Language
      English
      Type
      Article
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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.
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      http://hdl.handle.net/11693/22734
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.jnt.2009.01.007
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