Integrals Involving Associated Laguerre Polynomials

Orthogonal polynomials and their integrals are used for basis representations in physics problems. Integrals involving product of Hermite polynomials like,

was solved in [1]. A similar product of associated Laguerre polynomials

does not have a closed form expression. In this article we present a discrete sum formula for Eq.( 2), by using the following identities for the associated Laguerre polynomial and an integral formula [2],

The closed form expression of the overlap-integral is given by the nested sum, I a (p1,l1),(p2,l2),…,(pn,ln) = (p1,p2,…,pn)

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