A bibasic Heine transformation formula and Ramanujan's $_2\phi_1$ transformations
Combinatorics
2019-05-01 v3 Classical Analysis and ODEs
Abstract
We study Andrews and Berndt's organization of Ramanujan's transformation formulas in Chapter 1 of their book Ramanujan's Lost Notebook, Part II. In the process, we rediscover a bibasic Heine's transformation, which follows from a Fundamental Lemma given by Andrews in 1966, and obtain identities proximal to Ramanujan's entries. We also provide a multibasic generalization of Andrews' 1972 theorem concerning a -analogue of the Lauricella function. Our results only require the -binomial theorem, and are an application of what Andrews and Berndt call 'Heine's Method'.
Keywords
Cite
@article{arxiv.1606.05460,
title = {A bibasic Heine transformation formula and Ramanujan's $_2\phi_1$ transformations},
author = {Gaurav Bhatnagar},
journal= {arXiv preprint arXiv:1606.05460},
year = {2019}
}
Comments
Accepted for the proceedings of the Alladi 60th birthday conference. In this version, changes based on referee's comments, and some minor grammatical corrections