Polynomials Defined by Three-Term Recursion Relations and Satisfying a Second Recursion Relation: Connection with Discrete Integrability, Remarkable (Often Diophantine) Factorizations

DOI10.1142/S1402925111001416zbMath1229.33015OpenAlexW1552978377WikidataQ114072108 ScholiaQ114072108MaRDI QIDQ3018680

Francesco Calogero, Mario Bruschi, Riccardo Droghei

Publication date: 27 July 2011

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1402925111001416

zbMATH Keywords

orthogonal polynomialsrecursion relationsAskey schemediscrete integrabilityDiophantine factorizations

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 special orthogonal polynomials and functions (33C47)

Related Items (4)

Additional recursion relations, factorizations, and diophantine properties associated with the polynomials of the Askey scheme ⋮ Diophantine properties of orthogonal polynomials and rational functions ⋮ Properties of the zeros of the polynomials belonging to the \(q\)-Askey scheme ⋮ Properties of the zeros of generalized hypergeometric polynomials

Cites Work

• Integrable hierarchies of nonlinear difference-difference equations and symmetries
• Proof of certain Diophantine conjectures and identification of remarkable classes of orthogonal polynomials
• Nonlinear differential-difference equations, associated Backlund transformations and Lax technique
• A Nonlinear Difference Scheme and Inverse Scattering
• Tridiagonal matrices, orthogonal polynomials and Diophantine relations: II
• Tridiagonal matrices, orthogonal polynomials and Diophantine relations: I

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