Unit Circle Elliptic Beta Integrals

2003/09/30 by J. F. van Diejen, V. P. Spiridonov
Mathematics · #Advanced Mathematical Identities #Algebraic and Geometric Analysis #BETA (programming language) #Base (topology) #Computer science #Elliptic integral #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Mathematics education #Pure mathematics #Unit (ring theory) #Unit circle #math.CA #msc:33D99 #msc:33E20

paper · pdf · doi:10.1007/s11139-005-4846-x

published as The Ramanujan Journal 10, no 2 (2005), 187-204 · 15 pages; minor corrections, references updated, to appear in Ramanujan J

arxiv created 2005/07/28 · openalex publication_date 2005/10/01 · arxiv updated 2010/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present some elliptic beta integrals with a base parameter on the unit circle, together with their basic degenerations.

Citations

• First order analytic difference equations and integrable quantum systems
• The basic gamma-function and the elliptic functions
• The Elliptic Gamma Function and SL(3, Z)⋉Z3
• A course of modern analysis an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions
• Strongly Coupled Quantum Discrete Liouville Theory.¶I: Algebraic Approach and Duality
• Transformations of elliptic hypergometric integrals