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
q-Fibonacci Polynomials and the Rogers-Ramanujan Identities
✍ Scribed by Johann Cigler
- Publisher
- Springer
- Year
- 2004
- Tongue
- English
- Weight
- 224 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0218-0006
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We study the previously developed extension of the Engel expansion to the field of Formal Laurent series. We examine three separate aspects. First we consider the algorithm in relation to the work of Ramanujan. Second we show how the algorithm can be used to prove expansions such as those found by E
By LEONARD CARLITZ in Durham (N. C.) (Eingegangen am 5.3. 1957) 1. The ROGERS-RAMANUJAK identities (for proof and references see HARDY [2, Chapter 61) respectively. As HARDY remarks, the proofs of the identities are rather artificial. The object of the present note is to present a variant of ROGERS