Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. III: Associated continuous dual \(q\)-Hahn polynomials

DOI10.1016/0377-0427(95)00264-2zbMath0878.33011arXivmath/9411226OpenAlexW2093896893MaRDI QIDQ1919446

Mourad E. H. Ismail, David R. Masson, Dharma P. Gupta

Publication date: 1 December 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9411226

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Additive difference equations (39A10) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Continued fractions; complex-analytic aspects (30B70)

Related Items (16)

Interlacing properties and bounds for zeros of \({}_2\phi_1\) hypergeometric and little \(q\)-Jacobi polynomials ⋮ On basic Horn hypergeometric functions \(\mathrm{H}_3\) and \(\mathrm{H}_4\) ⋮ On quasi-orthogonal polynomials: their differential equations, discriminants and electrostatics ⋮ Contiguous relations and their computations for \(_2F_1\) hypergeometric series ⋮ Intertwiners of $U^{\prime }_q\bigl (\widehat{sl}(2)\bigr )$Uq′sl̂(2)-representations and the vector-valued big q-Jacobi transform ⋮ Contiguous relations for \(_{2}F_{1}\) hypergeometric series ⋮ One-parameter orthogonality relations for basic hypergeometric series ⋮ On some new contiguous relations for the Gauss hypergeometric function with applications ⋮ Contiguous function relations for \(k\)-hypergeometric functions ⋮ Wilson function transforms related to Racah coefficients ⋮ The Andrews-Stanley partition function and Al-Salam-Chihara polynomials ⋮ The vector-valued big \(q\)-Jacobi transform ⋮ Boundary matrices for the higher spin six vertex model ⋮ Unnamed Item ⋮ ON THE VALUES OF CONTINUED FRACTIONS: q-SERIES II ⋮ q 2-Kampé de Fériet series and sums of continuous dual q±2-Hahn polynomials

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• Contiguous relations, basic hypergeometric functions, and orthogonal polynomials. I
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• Recurrence relations, continued fractions, and orthogonal polynomials
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