Classical Orthogonal Polynomials of a Discrete Variable 1991
DOI: 10.1007/978-3-642-74748-9_2
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Classical Orthogonal Polynomials of a Discrete Variable

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Cited by 417 publications
(590 citation statements)
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“…from the differencial equation and Rodrigues formula for the Laguerre polynomials [4] we deduce the following properties for the Laguerre functions (25) i) differential equation…”
Section: Wave Equation For the Hidrogen Atom With Discrete Variablesmentioning
confidence: 96%
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“…from the differencial equation and Rodrigues formula for the Laguerre polynomials [4] we deduce the following properties for the Laguerre functions (25) i) differential equation…”
Section: Wave Equation For the Hidrogen Atom With Discrete Variablesmentioning
confidence: 96%
“…We have worked out general formulas for the differential/difference equation, recurrence relations, raising and lowering operators, commutation and anticommutation relations. The starting point is the general properties of classical orthogonal polynomials of continuous and discrete variable [4] of hypergeometric type, in particular the Rodrigues formula from which the raising and lowering operators are derived. Similar results were obtained with more sofisticated method using the factorization of the hamiltonian [6] [7].…”
Section: Introductionmentioning
confidence: 99%
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“…One underlying motivation of this series of works is to inaugurate a new theory for the Askey scheme of hypergeometric orthogonal polynomials [7][8][9][10] within the framework of QM. The abundant concepts and methods of QM accumulated over 80 years after the construction of QM would be available for the research of orthogonal polynomials.…”
Section: Introductionmentioning
confidence: 99%
“…When the polynomial sequence (P n ) n is classical discrete [28,29], i.e. orthogonal with respect to a positive weight function r defined on the set I ¼ {a; a þ 1; .…”
Section: Introductionmentioning
confidence: 99%