An equivalency of Bailey’s very-well-poised $_6\psi _6$ summation and Weierstrass’ theta function identity

DOI10.1090/proc/14438zbMath1475.33010OpenAlexW2900222040MaRDI QIDQ5384819

Jin Wang, Xin Rong Ma

Publication date: 26 June 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/14438

zbMATH Keywords

triple product identitybasic hypergeometric seriesWeierstrass' theta function identitysymmetric transformationBailey's \(_6\psi_6\) summationRogers' \(_6\phi_5\) summationvery-well-poised

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (1)

A common recursive formula for Ramanujan’s ₁𝜓₁ and Bailey’s very-well-poised ₆𝜓₆ summation formulas

Uses Software

• DLMF

Cites Work

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• Bailey's well-poised \(_{6}\psi _{6}\)-series implies the Askey-Wilson integral
• Bailey's very well-poised \(_6\psi_6\)-series identity
• Another proof of Bailey's \({}_6\psi_6\) summation
• A simple proof of Bailey’s very-well-poised ₆𝜓₆ summation
• On the equivalence of two fundamental theta identities
• Two Proofs of the ₆Ψ₆ Summation Theorem
• Applications of Basic Hypergeometric Functions
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• The Very Well Poised 6 ψ 6

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