Symmetries for Casorati determinants of classical discrete orthogonal polynomials

DOI10.1090/S0002-9939-2013-11802-2zbMath1284.42079MaRDI QIDQ5401673

Antonio J. Duran

Publication date: 11 March 2014

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

Full work available at URL: http://www.ams.org/journals/proc/2014-142-03/S0002-9939-2013-11802-2

zbMATH Keywords

orthogonal polynomialsdifference equationsMeixner polynomialsKrawtchouk polynomialsCharlier polynomialsHahn polynomialsCasorati determinantsdiscrete classical polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Other functions coming from differential, difference and integral equations (33E30)

Related Items (8)

Invariance properties of Wronskian type determinants of classical and classical discrete orthogonal polynomials ⋮ Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities ⋮ Exceptional Charlier and Hermite orthogonal polynomials ⋮ Random walk Green kernels in the neutral Moran model conditioned on survivors at a random time to origin ⋮ Exceptional Meixner and Laguerre orthogonal polynomials ⋮ Casorati type determinants of some $\mathfrak {q}$-classical orthogonal polynomials ⋮ The algebras of difference operators associated to Krall-Charlier orthogonal polynomials ⋮ Christoffel transform of classical discrete measures and invariance of determinants of classical and classical discrete polynomials

Cites Work

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• Using \(\mathcal D\)-operators to construct orthogonal polynomials satisfying higher order difference or differential equations
• On certain formulas of Karlin and Szegö
• The spectrum of symmetric Krawtchouk matrices
• Orthogonal polynomials satisfying higher-order difference equations
• Wronskian type determinants of orthogonal polynomials, Selberg type formulas and constant term identities
• On certain determinants whose elements are orthogonal polynomials
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Orthogonal Functions from Gram Determinants
• Orthogonal Polynomials Defined by Difference Equations

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