Proofs of the Rogers - RamanujanIdentities and of Identities of Similar
نویسنده
چکیده
New short and easy computer proofs of nite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the rst Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.
منابع مشابه
Easy Computer Proofs of the Rogers - RamanujanIdentities and of Identities of Similar
New short and easy computer proofs of nite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the rst Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.
متن کاملShort and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type
New short and easy computer proofs of finite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the first Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping. AMS Subject Classification. 05A19; secondary 11B65, 05A17
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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. Sc...
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Ramanujan’s lost notebook contains several identities arising from the Rogers–Fine identity and/or Rogers’ false theta functions. Combinatorial proofs for many of these identities are given.
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We evaluate several integrals involving generating functions of continuous q-Hermite polynomials in two diierent ways. The resulting identities give new proofs and generalizations of the Rogers-Ramanujan identities. Two quintic transformations are given, one of which immediately proves the Rogers-Ramanujan identities without the Jacobi triple product identity. Similar techniques lead to new tra...
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