Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials

DOI10.1016/j.jat.2014.03.016zbMath1318.33013arXiv1301.4887OpenAlexW2075474560MaRDI QIDQ2339497

Leandro Cagliero, Koornwinder, Tom H.

Publication date: 1 April 2015

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4887

zbMATH Keywords

Jacobi polynomialsGegenbauer polynomialsconnection coefficientsbiorthogonal systemAskey-Wilson polynomialsinverses of lower triangular matrices

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Inverse problems in linear algebra (15A29) Toeplitz, Cauchy, and related matrices (15B05)

Related Items (15)

Efficient spectral methods for some singular eigenvalue problems ⋮ Well-conditioned fractional collocation methods using fractional Birkhoff interpolation basis ⋮ Matrix-valued orthogonal polynomials related to the quantum analogue of \((\mathrm{SU}(2) \times \mathrm{SU}(2), \text{diag})\) ⋮ Disk polynomials and the one-dimensional wave equation ⋮ Dual addition formulas: the case of continuous \(q\)-ultraspherical and \(q\)-Hermite polynomials ⋮ Matrix-valued Gegenbauer-type polynomials ⋮ Fourier expansion of disk automorphisms via scattering in layered media ⋮ Duality and difference operators for matrix valued discrete polynomials on the nonnegative integers ⋮ Müntz ball polynomials and Müntz spectral-Galerkin methods for singular eigenvalue problems ⋮ Explicit matrix inverses for lower triangular matrices with entries involving continuous \(q\)-ultraspherical polynomials ⋮ A-posteriori error estimations of the GJF-Petrov-Galerkin methods for fractional differential equations ⋮ Generalized Jacobi functions and their applications to fractional differential equations ⋮ A new linear inversion formula for a class of hypergeometric polynomials ⋮ Optimal Fractional Integration Preconditioning and Error Analysis of Fractional Collocation Method Using Nodal Generalized Jacobi Functions ⋮ Matrix valued Hermite polynomials, Burchnall formulas and non-abelian Toda lattice

Uses Software

• DLMF

Cites Work

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• Fourier, Gegenbauer and Jacobi expansions for a power-law fundamental solution of the polyharmonic equation and polyspherical addition theorems
• Matrix-valued orthogonal polynomials related to \((\mathrm{SU}(2) \times \mathrm{SU}(2), \mathrm{diag})\). II
• INVERSION FORMULAS INVOLVING ORTHOGONAL POLYNOMIALS AND SOME OF THEIR APPLICATIONS
• New Proofs of Some q-Series Results
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• LU-decomposition of a noncommutative linear system and Jacobi polynomials
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Inverse Relations for Certain Sheffer Sequences
• The jacobi inversion formula

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