On Certain Generalizations of Rogers-Ramanujan Type Identities
Classical Analysis and ODEs
2016-02-02 v1
Abstract
We state and prove a number of unilateral and bilateral -series identities and explore some of their consequences. Those include certain generalizations of the -binomial sum which also generalize the -Airy function introduced by Ramanujan, as well as certain identities with an interesting variable-parameter symmetry based on limiting cases of Heine's transformation of basic hypergeomteric functions.
Cite
@article{arxiv.1602.00316,
title = {On Certain Generalizations of Rogers-Ramanujan Type Identities},
author = {Ahmad El-Guindy and Mourad E. H. Ismail},
journal= {arXiv preprint arXiv:1602.00316},
year = {2016}
}
Comments
9 pages, comments welcome