Legendre polynomials, Legendre--Stirling numbers, and the left-definite spectral analysis of the Legendre differential expression

DOI10.1016/S0377-0427(02)00582-4zbMath1014.33003OpenAlexW2071793397MaRDI QIDQ1860442

Lance L. Littlejohn, Richard Wellman, W. Norrie Everitt

Publication date: 23 February 2003

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(02)00582-4

zbMATH Keywords

Legendre polynomialsspectral theoremLegendre-Stirling numbersLagrangian symmetricleft-definite self-adjoint operatorleft-definite Sobolev space

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45)

Related Items (27)

Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression ⋮ Some positivities in certain triangular arrays ⋮ A matrix method for solving high-order linear difference equations with mixed argument using hybrid Legendre and Taylor polynomials ⋮ A combinatorial interpretation of the Legendre-Stirling numbers ⋮ On the spectra of left-definite operators ⋮ A note on the \(r\)-Whitney numbers of Dowling lattices ⋮ Total positivity properties of Jacobi-Stirling numbers ⋮ New family of Jacobi-Stirling numbers ⋮ Jacobi-Stirling polynomials and \(P\)-partitions ⋮ Characterization of self-adjoint ordinary differential operators ⋮ On certain combinatorial expansions of the Legendre-Stirling numbers ⋮ Solving high-order linear differential equations by a Legendre matrix method based on hybrid Legendre and Taylor polynomials ⋮ Glazman-Krein-Naimark theory, left-definite theory and the square of the Legendre polynomials differential operator ⋮ Hilbert scales and Sobolev spaces defined by associated Legendre functions ⋮ A connection between Jacobi-Stirling numbers and Bernoulli polynomials ⋮ Legendre-Stirling permutations ⋮ The Legendre-Stirling numbers ⋮ An asymptotic distribution theory for Eulerian recurrences with applications ⋮ On the nested sums and orthogonal polynomials ⋮ On Jacobi polynomials \(\mathscr{P}_k^{(\alpha,\beta)}\) and coefficients \(c_j^{\ell}(\alpha,\beta)\) \((k\geq 0, \ell =5,6; 1\leq j\leq \ell; \alpha,\beta > -1)\) ⋮ Legendre polynomial solutions of high-order linear Fredholm integro-differential equations ⋮ Unnamed Item ⋮ Legendre Collocation Method to Solve the Riccati Equations with Functional Arguments ⋮ \(\gamma\)-positivity and partial \(\gamma\)-positivity of descent-type polynomials ⋮ Left-definite theory with applications to orthogonal polynomials ⋮ New family of Whitney numbers ⋮ A note on the Jacobi–Stirling numbers

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• S-hermitesche Rand-Eigenwertprobleme. I
• No Continuum in E 2 Has the TMP. I. Arcs and Spheres
• ON SOME PROPERTIES OF THE LEGENDRE TYPE DIFFERENTIAL EXPRESSION
• Singular Sturm-Liouville Problems: The Friedrichs Extension and Comparison of Eigenvalues
• ON EXPANSIONS IN EIGENFUNCTIONS (II)
• Generating Functions for Bessel and Related Polynomials

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