A model for the continuous q-ultraspherical polynomials

DOI10.1063/1.530998zbMath0847.33010arXivmath/9504219OpenAlexW3104682049MaRDI QIDQ4873535

Luc Vinet, Roberto Floreanini

Publication date: 16 April 1996

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

Full work available at URL: https://arxiv.org/abs/math/9504219

zbMATH Keywords

Lie groupquantum groupsmatrix elements\(q\)-special functions\(q\)-ultraspherical polynomialsRoger's \(q\)-Hermite polynomials

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80) Applications of basic hypergeometric functions (33D90)

Related Items

A q-deformed e(4) and continuous q-Jacobi polynomials, Spectral properties and a Parseval's equality in the singular case for \(q\)-Dirac problem, On a $q$-analogue of the Sturm-Liouville operator with discontinuity conditions, Basic-deformed quantum mechanics, Orthogonality and completeness of \(q\)-Fourier type systems, Titchmarsh–Weyl theory for q-Dirac systems, Inverse operators, \(q\)-fractional integrals, and \(q\)-Bernoulli polynomials

Cites Work

• Symmetry techniques for q-series: Askey-Wilson polynomials
• Diagonalization of certain integral operators
• Quantum algebras and \(q\)-special functions
• \(q\)-orthogonal polynomials and the oscillator quantum group
• Generalized q-Bessel functions
• The Basic Bessel Functions and Polynomials
• Addition formulas for q-Bessel functions
• A quantum algebra approach to basic multivariable special functions
• Special Functions and the Complex Euclidean Group in 3-Space. I