𝑞-difference operators, orthogonal polynomials, and symmetric expansions

DOI10.1090/memo/0757zbMath1018.33014OpenAlexW2055512083MaRDI QIDQ3151295

Douglas Bowman

Publication date: 8 October 2002

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0757

zbMATH Keywords

orthogonal polynomials\(q\)-seriesbasic hypergeometric functions\(q\)-difference equationsspecial functions

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Other basic hypergeometric functions and integrals in several variables (33D70)

Related Items (11)

On constructing solutions for the functional equation \(Z(x, y, n) = Z(a_{11} x + a_{12} y, a_{21} x + a_{22} y, n + 1)\) ⋮ \(q\)-difference equation and \(q\)-polynomials ⋮ Bivariate generating functions for Rogers-Szegö polynomials ⋮ On asymptotic approximations of first integrals for second order difference equations ⋮ Extensions of \(q\)-Chu-Vandermonde's identity ⋮ Applications of a generalized \(q\)-difference equation ⋮ Generalizations of Milne’s U(n + 1) q-Chu-Vandermonde summation ⋮ Elements of the theory of stability of hybrid systems (review) ⋮ New proofs of generating functions for Rogers-Szegö polynomials ⋮ An easy proof of the Askey-Wilson integral and applications of the method ⋮ Some new generating functions for \(q\)-Hahn polynomials

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