A basic class of symmetric orthogonal functions with six free parameters

DOI10.1016/j.cam.2009.12.025zbMath1195.33068OpenAlexW1994516082MaRDI QIDQ964950

Mohammad Masjed-Jamei

Publication date: 21 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.cam.2009.12.025

zbMATH Keywords

generalized Hermite polynomialsFavard's theoremextended Sturm-Liouville theorem for symmetric functionsgeneralized ultraspherical polynomialssymmetric orthogonal functionstwo sequences of finite classical symmetric orthogonal polynomials

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Sturm-Liouville theory (34B24) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Other special orthogonal polynomials and functions (33C47)

Related Items (9)

On a symmetric generalization of bivariate Sturm-Liouville problems ⋮ A class of symmetric \(q\)-orthogonal polynomials with four free parameters ⋮ A basic class of symmetric orthogonal polynomials of a discrete variable ⋮ A symmetric generalization of Sturm-Liouville problems in \(q\)-difference spaces ⋮ A symmetric sequence of trigonometric orthogonal functions ⋮ Incomplete symmetric orthogonal polynomials of finite type generated by a generalized Sturm–Liouville theorem ⋮ An extension of Pochhammer’s symbol and its application to hypergeometric functions ⋮ A symmetric generalization of Sturm–Liouville problems in discrete spaces ⋮ On generating symmetric orthogonal polynomials

Cites Work

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• On incomplete symmetric orthogonal polynomials of Jacobi type
• Sieved Ultraspherical Polynomials
• Classical orthogonal polynomials with weight function ((ax + b)² + (cx + d)²)^−pexp(qArctg((ax + b)/(cx + d))),x ∈ (−∞, ∞) and a generalization of T and F distributions
• On the complete solution of the Sturm–Liouville problem (d2X/dx2)+λ2X=0 over a closed interval
• A generalization of classical symmetric orthogonal functions using a symmetric generalization of Sturm–Liouville problems
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