Solution of an open problem about two families of orthogonal polynomials

DOI10.3842/SIGMA.2019.005zbMath1412.42068arXiv1901.09332OpenAlexW2914276105WikidataQ128456705 ScholiaQ128456705MaRDI QIDQ2633018

Walter Van Assche

Publication date: 8 May 2019

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.09332

zbMATH Keywords

orthogonal polynomialsspecial functionsopen problems

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 (7)

Progressive approximation of bound states by finite series of square-integrable functions ⋮ Open problem in orthogonal polynomials ⋮ Bound states and the potential parameter spectrum ⋮ Deformed Morse-like potential ⋮ Bound states of an inverse-cube singular potential: A candidate for electron-quadrupole binding ⋮ Exponentially confining potential well ⋮ Recurrence equations and their classical orthogonal polynomial solutions on a quadratic or a q-quadratic lattice

Uses Software

• DLMF
• retode

Cites Work

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• Compact Jacobi matrices: From Stieltjes to Krein and \(M(a,b)\)
• An extended class of \(L^2\)-series solutions of the wave equation
• NIST digital library of mathematical functions
• Recurrence equations and their classical orthogonal polynomial solutions
• Orthogonal polynomials derived from the tridiagonal representation approach
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Series solutions of Heun-type equation in terms of orthogonal polynomials
• Reconstructing the Potential Function in a Formulation of Quantum Mechanics Based on Orthogonal Polynomials
• Recurrence equations and their classical orthogonal polynomial solutions on a quadratic or a q-quadratic lattice
• Solution of the nonrelativistic wave equation using the tridiagonal representation approach
• Quantum mechanics without potential function
• Extending the class of solvable potentials. I. The infinite potential well with a sinusoidal bottom

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