Results on the associated classical orthogonal polynomials

DOI10.1016/0377-0427(95)00112-3zbMath0849.33006OpenAlexW1974657110MaRDI QIDQ1917943

Stanisław Lewanowicz

Publication date: 7 November 1996

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

Full work available at URL: https://doi.org/10.1016/0377-0427(95)00112-3

zbMATH Keywords

associated orthogonal 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)

Related Items (14)

Construction of recurrences for the coefficients of expansions in \(q\)-classical orthogonal polynomials ⋮ On the fourth-order difference equation for the associated Meixner polynomials ⋮ Recurrence relations for the connection coefficients of classical orthogonal polynomials ⋮ Second-order recurrence relation for the linearization coefficients of the classical orthogonal polynomials ⋮ Fast associated classical orthogonal polynomial transforms ⋮ Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials. ⋮ Factorization of self-adjoint ordinary differential equations ⋮ The fourth-order difference equation satisfied by the associated orthogonal polynomials of the \(\Delta\)-Laguerre-Hahn class ⋮ The fourth-order difference equation satisfied by the associated orthogonal polynomials of the Dq-Laguerre - Hahn Class ⋮ Fourth-order difference equation satisfied by the co-recursive of \(q\)-classical orthogonal polynomials ⋮ Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable ⋮ Fourth-order difference equation for the associated classical discrete orthogonal polynomials ⋮ Connection problems for polynomial solutions of nonhomogeneous differential and difference equations ⋮ Fourth order \(q\)-difference equation for the first associated of the \(q\)-classical orthogonal polynomials

Uses Software

• Maple

Cites Work

• Co-recursive orthogonal polynomials and fourth-order differential equation
• Quick construction of recurrence relations for the Jacobi coefficients
• Results on the associated Jacobi and Gegenbauer polynomials
• Fourth-order differential equation satisfied by the associated of any order of all classical orthogonal polynomials. A study of their distribution of zeros
• Classical orthogonal polynomials: A functional approach
• The three-term recurrence relation and the differentiation formulas for hypergeometric-type functions
• Recurrence relations for connection coefficients between two families of orthogonal polynomials
• Associated Laguerre and Hermite polynomials
• Properties of the Polynomials Associated with the Jacobi Polynomials
• Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
• Fourth-order differential equations for numerator polynomials
• ON A CHARACTERIZATION OF MEIXNER'S POLYNOMIALS
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