Summation formulae for the bilateral basic hypergeometric series ₁ψ₁ ( a; b; q, z )

2016/03/22 by Hironori Mori, Mori, Hironori, Takeshi Morita +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1603.06657

openalex publication_date 2016/03/22 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We give summation formulae for the bilateral basic hypergeometric series ₁ψ₁( a; b; q, z ) through Ramanujan's summation formula, which are generalizations of nontrivial identities found in the physics of three-dimensional Abelian mirror symmetry on RP² × S¹. We also show the q → 1 - 0 limit of our summation formulae.

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