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arxiv: 1606.05460 · v3 · pith:QHA334QHnew · submitted 2016-06-17 · 🧮 math.CO · math.CA

A bibasic Heine transformation formula and Ramanujan's ₂φ₁ transformations

classification 🧮 math.CO math.CA
keywords andrewsramanujanheinetransformationberndtbibasictheoremanalogue
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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'.

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