Connection problems via lowering operators

Authors:
Y. Ben Cheikh;H. Chaggara
Affiliations:
Département de Mathématiques, Faculté des Sciences de Monastir, 5019 Monastir, Tunisie;Département de Préparation en Math-Physique, Institut préparatoire aux études d'ingénieur de Monastir, 5019 Monastir, Tunisie
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the seventh international symposium on Orthogonal polynomials, special functions and applications
Year:
2005

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Abstract

The lowering operator σ associated with a polynomial set {Pn}n ≥ 0 is an operator not depending on n and satisfying the relation σ(Pn) = nPn-1. In this paper, we express explicitly the connection coefficients between two polynomial sets using their corresponding lowering operators. We obtain some well-known results as particular cases including some duplication and addition formulas.