A model for the continuous q-ultraspherical polynomials
Copyright policy )A model for the continuous q-ultraspherical polynomials
An algebraic interpretation for two classes of continuous q-polynomials is provided. Rogers’ continuous q-Hermite polynomials and continuous q-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the q-Heisenberg algebra and a q-deformation of the Euclidean algebra in these dimensions. A generating function for the continuous q-Hermite polynomials and a q-analog of the Fourier–Gegenbauer expansion are naturally obtained from these models.
- University of Montreal Canada
- University of Trieste Italy
- National Institute for Nuclear Physics Italy
quantum groups, matrix elements, Quantum groups (quantized enveloping algebras) and related deformations, Lie group, Basic hypergeometric functions in one variable, \({}_r\phi_s\), \(q\)-special functions, Roger's \(q\)-Hermite polynomials, Mathematics - Classical Analysis and ODEs, \(q\)-ultraspherical polynomials, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Applications of basic hypergeometric functions, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Quantum groups and related algebraic methods applied to problems in quantum theory
quantum groups, matrix elements, Quantum groups (quantized enveloping algebras) and related deformations, Lie group, Basic hypergeometric functions in one variable, \({}_r\phi_s\), \(q\)-special functions, Roger's \(q\)-Hermite polynomials, Mathematics - Classical Analysis and ODEs, \(q\)-ultraspherical polynomials, Mathematics - Quantum Algebra, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Quantum Algebra (math.QA), Applications of basic hypergeometric functions, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Quantum groups and related algebraic methods applied to problems in quantum theory
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