The Laguerre Constellation of Classical Orthogonal Polynomials

Roberto S. Costas-Santos ()
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Roberto S. Costas-Santos: Department of Quantitative Methods, Universidad Loyola Andalucía, 41704 Sevilla, Spain

Mathematics, 2025, vol. 13, issue 2, 1-18

Abstract: A linear functional u is classical if there exist polynomials ϕ and ψ with deg ϕ ≤ 2 and deg ψ = 1 such that D ϕ ( x ) u = ψ ( x ) u , where D is a certain differential, or difference, operator. The polynomials orthogonal with respect to the linear functional u are called classical orthogonal polynomials. In the theory of orthogonal polynomials, a correct characterization of the classical families is of great interest. In this work, on the one hand, we present the Laguerre constellation, which is formed by all the classical families for which deg ϕ = 1 , obtaining for all of them new algebraic identities such as structure formulas and orthogonality properties, as well as new Rodrigues formulas; on the other hand, we present a theorem that characterizes the classical families belonging to the Laguerre constellation.

Keywords: recurrence relation; characterization theorem; classical orthogonal polynomials; Laguerre constellation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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