Fourth-order differential equations satisfied by the generalized co- recursive of all classical orthogonal polynomials. A study of their distribution of zeros

DOI10.1016/0377-0427(94)00006-MzbMath0835.42013MaRDI QIDQ1899987

A. Zarzo, Eduardo Paciência Godoy, André Ronveaux

Publication date: 1 April 1996

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

zbMATH Keywords

orthogonal polynomialsMathematicadistribution of zerosfourth-order differential equationco-recursive

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) Real polynomials: location of zeros (26C10)

Related Items (14)

Difference equations for the co-recursive \(r\)th associated orthogonal polynomials of the \(D _{q}\)-Laguerre-Hahn class. ⋮ Fast algorithms using orthogonal polynomials ⋮ Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Continuous case ⋮ Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Discrete case ⋮ Modified Clebsch-Gordan-type expansions for products of discrete hypergeometric polynomials ⋮ A general method for deriving some semi-classical properties of perturbed second degree forms: the case of the Chebyshev form of second kind ⋮ Generalized Hermite polynomials associated with functions of parabolic cylinder ⋮ Factorization of fourth-order differential equations for perturbed classical orthogonal polynomials. ⋮ The fourth-order difference equation satisfied by the associated orthogonal polynomials of the Dq-Laguerre - Hahn Class ⋮ Decomposition of perturbed Chebyshev polynomials ⋮ Fourth-order difference equation satisfied by the co-recursive of \(q\)-classical orthogonal polynomials ⋮ Computation of Newton sum rules for associated and co-recursive classical orthogonal polynomials ⋮ Orthogonal polynomials---centroid of their zeroes ⋮ Rediscovering the contributions of Rodrigues on the representation of special functions

Uses Software

• Mathematica

Cites Work

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