Orthogonality of the Jacobi polynomials with negative integer parameters

DOI10.1016/S0377-0427(01)00589-1zbMath1002.42016MaRDI QIDQ1612413

María Álvarez de Morales, M. Luisa Rezola, Manuel Alfaro

Publication date: 22 August 2002

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

zbMATH Keywords

Jacobi polynomialsSobolev orthogonality

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 (18)

Approximation by polynomials in Sobolev spaces with Jacobi weight ⋮ Approximation and orthogonality in Sobolev spaces on a triangle ⋮ Nonclassical Jacobi polynomials and Sobolev orthogonality ⋮ Approximation by polynomials in Sobolev spaces associated with classical moment functionals ⋮ A new approach to the asymptotics of Sobolev type orthogonal polynomials ⋮ The numerical solution of fractional integral equations via orthogonal polynomials in fractional powers ⋮ On Sobolev orthogonal polynomials ⋮ Characterizations of distributional weights for weak orthogonal polynomials satisfying a second-order differential equation ⋮ On Sobolev bilinear forms and polynomial solutions of second-order differential equations ⋮ Classical and Sobolev orthogonality of the nonclassical Jacobi polynomials with parameters \(\alpha =\beta =-1\) ⋮ Non-classical orthogonality relations for big and little \(q\)-Jacobi polynomials ⋮ New orthogonality relations for the continuous and the discrete \(q\)-ultraspherical polynomials ⋮ An extended class of orthogonal polynomials defined by a Sturm-Liouville problem ⋮ Orthogonality of \(q\)-polynomials for non-standard parameters ⋮ Characterization of orthogonal polynomials— A new proof of Bochner’s theorem ⋮ Extensions of discrete classical orthogonal polynomials beyond the orthogonality ⋮ Orthogonal polynomials and partial differential equations on the unit ball ⋮ Linear interpolation and Sobolev orthogonality

Cites Work

• Sobolev orthogonal polynomials and second-order differential equations
• Sobolev orthogonality for the Gegenbauer polynomials \(\{ C_n^{-N+1/2}\}_{n\geq 0}\)
• Sobolev orthogonal polynomials: The discrete-continuous case
• On Sobolev orthogonality for the generalized Laguerre polynomials
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