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

DOI10.1090/proc/16434zbMath1527.33014MaRDI QIDQ6083345

Xin Rong Ma, Jin Wang

Publication date: 31 October 2023

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

zbMATH Keywords

basic hypergeometric seriestelescoping methodRamanujan's \(_1\psi_1\) summation formulaWeierstrass' theta identityvery-well-poisedBailey's VWP \(_6\psi_6\) summation formulabilateral truncated sum

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)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The truncated pentagonal number theorem
• A truncated Jacobi triple product theorem
• Bilateral truncated Jacobi's identity
• Truncated theta series and a problem of Guo and Zeng
• Two truncated identities of Gauss
• Truncated Jacobi triple product series
• Truncated Hecke-Rogers type series
• Bailey's very well-poised \(_6\psi_6\)-series identity
• Abel's lemma on summation by parts and Ramanujan's \(_1\psi_1\)-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
• Partial sums of Bailey's₆ψ₆-series to faster convergent series
• Two Proofs of the ₆Ψ₆ Summation Theorem
• Chapter 16 of Ramanujan’s second notebook: theta-functions and 𝑞-series
• Applications of Basic Hypergeometric Functions
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• The Very Well Poised 6 ψ 6
• The very well Poised 6 ψ 6 . II
• A new elliptic interpolation formula via the $(f,g)$-inversion
• An equivalency of Bailey’s very-well-poised $_6\psi _6$ summation and Weierstrass’ theta function identity
• The Abel Lemma and the $q$-Gosper Algorithm
• SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS

This page was built for publication: A common recursive formula for Ramanujan’s ₁𝜓₁ and Bailey’s very-well-poised ₆𝜓₆ summation formulas