q-Integral and Moment Representations for q-Orthogonal Polynomials

DOI10.4153/CJM-2002-027-2zbMath1009.33015MaRDI QIDQ3153534

Mourad E. H. Ismail, Dennis W. Stanton

Publication date: 7 April 2003

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

generating functions\(q\)-orthogonal polynomials\(q\)-integralAl-Salam-Chihara polynomials\(q\)-Pollaczek polynomialscontinuous \(q\)-Hermite polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Moment problems and interpolation problems in the complex plane (30E05) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (20)

Applications of \(q\)-Taylor theorems ⋮ Probabilistic aspects of Al-Salam–Chihara polynomials ⋮ New Integral Equations for the Monic Hermite Polynomials ⋮ Recurrence relations for the moments of discrete semiclassical orthogonal polynomials ⋮ q-Difference equations of moment integrals for transformational identities and generating functions ⋮ Orthogonal polynomials associated with a continued fraction of Hirschhorn ⋮ Utility of integral representations for basic hypergeometric functions and orthogonal polynomials ⋮ Moments for generating functions of Al-Salam-Carlitz polynomials ⋮ Towards a \(q\)-analogue of the Kibble-Slepian formula in 3 dimensions ⋮ One-parameter orthogonality relations for basic hypergeometric series ⋮ New family of symmetric orthogonal polynomials and a solvable model of a kinetic spin chain ⋮ ON SUMMABLE, POSITIVE POISSON–MEHLER KERNELS BUILT OF AL-SALAM–CHIHARA AND RELATED POLYNOMIALS ⋮ A note on moment integrals and some applications ⋮ Determinants with orthogonal polynomial entries ⋮ Quadratic harnesses, $q$-commutations, and orthogonal martingale polynomials ⋮ A moment problem and a family of integral evaluations ⋮ Unnamed Item ⋮ Solutions of the Al-Salam–Chihara and allied moment problems ⋮ Jacobi polynomial moments and products of random matrices ⋮ ALTERNATIVE PROOFS OF GENERATING FUNCTIONS FOR HAHN POLYNOMIALS AND SOME APPLICATIONS

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