A bibasic Heine transformation formula and Ramanujan's $_2ϕ_1$ transformations
Year: 2016
Type: preprint
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 $q$-analogue of the Lauricella function. Our results only require the $q$-binomial theorem, and are an application of what Andrews and Berndt call 'Heine's Method'.
Source: arXiv (Cornell University)
Author: Bhatnagar, Gaurav
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
Award: G345047177
OpenAlex ID: W4302197029