Hyperbolic beta integrals

DOI10.1016/j.aim.2003.12.003zbMath1072.33012arXivmath/0303178OpenAlexW2104392597MaRDI QIDQ703801

Jasper V. Stokman

Publication date: 11 January 2005

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0303178

zbMATH Keywords

Askey-Wilson beta integralhyperbolic beta integralshyperbolic gamma functionMacdonald-Mehta integralNassrallah-Rahman beta integralRamanujan beta integral

Mathematics Subject Classification ID

(q)-gamma functions, (q)-beta functions and integrals (33D05) Bibasic functions and multiple bases (33D65)

Related Items

Properties of generalized univariate hypergeometric functions ⋮ Integrable quad equations derived from the quantum Yang-Baxter equation ⋮ General modular quantum dilogarithm and beta integrals ⋮ The star-triangle relation, lens partition function, and hypergeometric sum/integrals ⋮ Two-component Yang-Baxter maps and star-triangle relations ⋮ The endless beta integrals ⋮ Elliptic hypergeometric sum/integral transformations and supersymmetric lens index ⋮ The hyperbolic asymptotics of elliptic hypergeometric integrals arising in supersymmetric gauge theory ⋮ A relativistic hypergeometric function ⋮ Limits of elliptic hypergeometric integrals ⋮ Unit circle elliptic beta integrals ⋮ Complex hypergeometric functions and integrable many-body problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• More q-beta integrals
• On elliptic product formulas for Jackson integrals associated with reduced root systems
• On certain multiple Bailey, Rogers and Dougall type summation formulas
• From double Hecke algebra to Fourier transform
• An expansion formula for the Askey-Wilson function
• One-dimensional double Hecke algebra and Gaussian sums
• A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type
• Spectral transformation chains and some new biorthogonal rational functions
• A generalized hypergeometric function. III: Associated Hilbert space transform
• Unit circle elliptic beta integrals
• INTEGRAL SOLUTIONS OF HYPERGEOMETRIC q-DIFFERENCE SYSTEMS WITH |q| = 1
• On the elliptic beta function
• A generalization of Selberg’s beta integral
• Projection Formulas, a Reproducing Kernel and a Generating Function for q-Wilson Polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• An integral Representation of a ₁₀ϕ₉ and Continuous Bi-Orthogonal ₁₀ϕ₉ Rational Functions
• Two Integrals of Ramanujan
• Some q-Beta and Mellin-Barnes Integrals on Compact Lie Groups and Lie Algebras
• First order analytic difference equations and integrable quantum systems