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 RogersแRamanujan identities. Two quintic transformations are given, one of which immediately proves the RogersแR
A graphic illustration of Rogers-Ramanujan Identities
โ Scribed by K.K. Nambiar
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 188 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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
## 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