Some Integrals of the products of laguerre polynomials

Abstract

The evaluation of an integral of the product of Laguerre polynomials was discussed recently in this Journal by Mavromatis [12] (1990) and Lee [9] (1997) [see also Ong and Lee [14] (2000)]. The main object of the present sequel to these earlier works is to consider a family of such integrals of the products of Laguerre, Hermite, and other classical orthogonal polynomials in a systematic and unified manner. Relevant connections of some of these integral formulas with various known integrals, as well as the computational and numerical aspects of the results presented here, are also pointed out.

Keywords:

• Laguerre polynomials
• Hermite polynomials
• Classical orthogonal polynomials
• Generalized hypergeometric functions
• Lauricella functions
• Appell functions
• Kampé de Fériet functions
• Hypergeometric polynomials
• Laplace transforms
• Jacobi polynomials
• Pfaff-Saalschutz theorem
• Gegenbauer (or ultraspherical) polynomials
• Polynomial expansions
• (Clebsch-Gordan) linearization formulas
• Recurrence relations

2000 Matheamtics Subject Classifications: Primary:

• 33C20
• 33C45

C.R. Categories:

• G1.4

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Notes

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