Properties of generalized univariate hypergeometric functions

DOI10.1007/s00220-007-0289-0zbMath1144.33007arXivmath/0607250OpenAlexW1965522990MaRDI QIDQ2384770

Jasper V. Stokman, Eric M. Rains, Fokko J. van de Bult

Publication date: 10 October 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607250

Mathematics Subject Classification ID

Other hypergeometric functions and integrals in several variables (33C70) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)

Related Items (22)

Relations among complementary and supplementary pairings of Saalschützian \(_4F_3(1)\) series ⋮ Introduction to the theory of elliptic hypergeometric integrals ⋮ Coxeter group actions and limits of hypergeometric series ⋮ \(3d\) dualities from \(4d\) dualities ⋮ Relations for a class of terminating ₄F₃(4) hypergeometric series ⋮ Elliptic hypergeometric functions and Calogero-Sutherland-type models ⋮ A ``Lagrangian for the \(E_7\) superconformal theory ⋮ Representation of the quantum plane, its quantum double, and harmonic analysis on \(GL_q^+(2,\mathbb{R })\) ⋮ Elliptic hypergeometry of supersymmetric dualities. II: Orthogonal groups, knots, and vortices ⋮ General modular quantum dilogarithm and beta integrals ⋮ The star-triangle relation, lens partition function, and hypergeometric sum/integrals ⋮ Entanglement entropy of ABJM theory and entropy of topological black hole ⋮ Coxeter group actions on \({}_{4} F_{3}(1)\) hypergeometric series ⋮ A parafermionic hypergeometric function and supersymmetric \(6j\)-symbols ⋮ Coxeter group actions on Saalschützian \(_4F_3(1)\) series and very-well-poised \(_7F_6(1)\) series ⋮ The endless beta integrals ⋮ Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group ⋮ The Virasoro fusion kernel and Ruijsenaars' hypergeometric function ⋮ The problem of the moody chess players ⋮ On a family of integrals that extend the Askey-Wilson integral ⋮ Limits of elliptic hypergeometric integrals ⋮ Complex hypergeometric functions and integrable many-body problems

Cites Work

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• Hyperbolic beta integrals
• Limits of elliptic hypergeometric integrals
• Galois theory of difference equations
• Difference Fourier transforms for nonreduced root systems
• Elliptic U(2) quantum group and elliptic hypergeometric series
• Orthogonal polynomials associated with root systems
• Fourier transforms on the quantum \(\text{SU}(1,1)\) group. (With an appendix by Mizan Rahman).
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• Quantum zonal spherical functions and Macdonald polynomials
• A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type
• Spectral transformation chains and some new biorthogonal rational functions
• Short proofs of the elliptic beta integrals
• Symmetry groups of Bailey's transformations for \(_{10}\phi _{9}\)-series
• Ruijsenaars' hypergeometric function and the modular double of \(\mathcal {U}_{q}(\mathfrak {sl}_{2}(\mathbb C))\)
• A generalized hypergeometric function. II: Asymptotics and \(D_4\) symmetry
• A generalized hypergeometric function. III: Associated Hilbert space transform
• On the elliptic beta function
• Projection Formulas, a Reproducing Kernel and a Generating Function for q-Wilson Polynomials
• An integral Representation of a ₁₀ϕ₉ and Continuous Bi-Orthogonal ₁₀ϕ₉ Rational Functions
• The Associated Askey-Wilson Polynomials
• Quantum integrability of the generalized elliptic Ruijsenaars models
• Integrability of difference Calogero–Moser systems
• First order analytic difference equations and integrable quantum systems
• Contiguous relations, continued fractions and orthogonality

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