Browsing by Subject "Theta functions"

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    Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions
    (Elsevier, 2012) Yesilyurt, H.
    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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    Modular equations of degrees 13, 29, and 61
    (Springer New York LLC, 2023-11-21) Güloğlu, Ahmet M.; Yesilyurt, Hamza
    Schröter-type theta function identities were very instrumental in proving modular equations. In this paper, by employing a generalization of this identity, we prove for the first time a modular equation of degree 61. Furthermore, new modular equations of degrees 13 and 29 are obtained.