Hypergeometric type \(q\)-difference equations: Rodrigues type representation for the second kind solution

DOI10.1016/j.cam.2004.02.018zbMath1067.39033OpenAlexW2090558690MaRDI QIDQ704175

A. Zarzo, Eduardo Paciência Godoy, IvÁn Area, André Ronveaux

Publication date: 13 January 2005

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

Full work available at URL: https://doi.org/10.1016/j.cam.2004.02.018

zbMATH Keywords

recurrence relationOrthogonal polynomialsFunctions of the second kindRodrigues type representationsSecond-order \(q\)-difference equations of hypergeometric type

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Generalized hypergeometric series, ({}_pF_q) (33C20) Difference equations, scaling ((q)-differences) (39A13)

Related Items (8)

Adjoint difference equation for the Nikiforov-Uvarov-Suslov difference equation of hypergeometric type on non-uniform lattices ⋮ Small divisor problem in dynamical systems and analytic solutions of a \(q\)-difference equation with a singularity at the origin ⋮ On the complex difference equation of hypergeometric type on non-uniform lattices ⋮ Gaussian integration formulas for logarithmic weights and application to 2-dimensional solid-state lattices ⋮ Functions of the second kind for classical polynomials ⋮ Generalizations of Rodrigues type formulas for hypergeometric difference equations on nonuniform lattices ⋮ Small divisor problem for an analytic \(q\)-difference equation ⋮ Extensions of some results of P. Humbert on Bezout's identity for classical orthogonal polynomials

Cites Work

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• Fourth order \(q\)-difference equation for the first associated of the \(q\)-classical orthogonal polynomials
• Hypergeometric-type differential equations: second kind solutions and related integrals.
• A fourth order \(q\)-difference equation for associated discrete \(q\)-orthogonal polynomials.
• Representations for the first associated \(q\)-classical orthogonal polynomials
• On classical orthogonal polynomials
• Inversion problems in the \(q\)-Hahn tableau
• The theory of difference analogues of special functions of hypergeometric type
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
• Quantum calculus

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