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Variants of the Rogers–Ramanujan Identities

✍ Scribed by Kristina Garrett; Mourad E.H. Ismail; Dennis Stanton

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
176 KB
Volume
23
Category
Article
ISSN
0196-8858

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✦ Synopsis

We evaluate several integrals involving generating functions of continuous q-Hermite polynomials in two different 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 transformations for unilateral and bilateral series. The quintic transformations lead to curious identities involving primitive fifth roots of unity which are then extended to primitive pth roots of unity for odd p.

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