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

✍ Scribed by Hamza Yesilyurt


Book ID
113721701
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
217 KB
Volume
388
Category
Article
ISSN
0022-247X

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Variants of the Rogers–Ramanujan Identit
✍ Kristina Garrett; Mourad E.H. Ismail; Dennis Stanton 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 176 KB

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᎐R