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On identities of the Rogers-Ramanujan type

✍ Scribed by Peter Paule

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
980 KB
Volume
107
Category
Article
ISSN
0022-247X

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A Note on the Rogers-Ramanujan identitie
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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

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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

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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

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✍ S. Ole Warnaar 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 186 KB

## dedicated to barry mccoy on the occasion of his 60th birthday A new polynomial analogue of the Rogers-Ramanujan identities is proven. Here the product-side of the Rogers-Ramanujan identities is replaced by a partial theta sum and the sum-side by a weighted sum over Schur polynomials. # 2002 Els