On $BC$ type basic hypergeometric orthogonal polynomials
Copyright policy )On $BC$ type basic hypergeometric orthogonal polynomials
The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with respect to an explicit (in general complex) measure. A partially discrete orthogonality measure is obtained by shifting the contour to the torus while picking up residues. A parameter domain is given for which the partially discrete orthogonality measure is positive. The orthogonality relations and norm evaluations for multivariable q-Racah polynomials and multivariable big and little q-Jacobi polynomials are proved by taking suitable limits in the orthogonality relations for the multivariable Askey-Wilson polynomials. In particular new proofs of several well known q-analogues of the Selberg integral are obtained.
AMS-LaTeX v1.2, 53 pages, no figures
- Panthéon-Assas University France
- University of Amsterdam Netherlands
- University of Paris France
- University of Paris France
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), multivariable basic hypergeometric orthogonal polynomials, 33D45 (Primary) 33D25 (Secondary), Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Mathematics - Quantum Algebra, multivariable \(q\)-Racah polynomials, FOS: Mathematics, Quantum Algebra (math.QA), multivariable big and little \(q\)-Jacobi polynomials, residue calculus, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Koornwinder polynomials, \(q\)-Selberg type integrals
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), multivariable basic hypergeometric orthogonal polynomials, 33D45 (Primary) 33D25 (Secondary), Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Mathematics - Quantum Algebra, multivariable \(q\)-Racah polynomials, FOS: Mathematics, Quantum Algebra (math.QA), multivariable big and little \(q\)-Jacobi polynomials, residue calculus, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Koornwinder polynomials, \(q\)-Selberg type integrals
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