Identities for families of orthogonal polynomials and special functions

DOI10.1080/10652469708819127zbMath0895.33002OpenAlexW2051090703MaRDI QIDQ4349690

Wolfram Koepf

Publication date: 2 September 1998

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469708819127

zbMATH Keywords

orthogonal polynomialsJacobi polynomialscomputer algebraGegenbauer polynomialsLaguerre polynomialsMeixner polynomialsKrawtchouk polynomialsCharlier polynomialsWhittaker functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items

Some identities of Laguerre polynomials arising from differential equations ⋮ A note on parameter derivatives of the Jacobi polynomials on the triangle ⋮ On parameter derivatives of a family of polynomials in two variables ⋮ Representations for parameter derivatives of some Koornwinder polynomials in two variables ⋮ Representations of orthogonal polynomials ⋮ On the solutions of holonomic third-order linear irreducible differential equations in terms of hypergeometric functions ⋮ Explicit form for the kernel operator matrix elements in eigenfunction basis of harmonic oscillator ⋮ Derivations and identities for Kravchuk polynomials ⋮ Explicit formulae for integro-differential operational matrices ⋮ The derivative connecting problems for some classical polynomials ⋮ Classical orthogonal polynomials: Dependence of parameters ⋮ Inner bounds for the extreme zeros of ₃F₂ hypergeometric polynomials

Uses Software

• gfun
• OrthogonalPolynomials
• REDUCE
• NCPOLY

Cites Work

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• GFUN
• REDUCE package for the indefinite and definite summation
• Bounded nonvanishing functions and bateman functions