Séminaire Lotharingien de Combinatoire, B14Sc (1986).

Joe Gillis, J. Jedwab an Doron Zeilberger

A Combinatorial Interpretation of the Integral of the Product of Legendre Polynomials

Abstract. We obtain in an explicit manner an interpretation of the integral of the product of k Legendre polynomials in terms of a sum involving binomial coefficients. A further interpretation is given by means of a combinatorial model. Some special cases are treated whose consequences lead to certain interesting new combinatorial identities.

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The paper has been finally published under the same title in SIAM J. Math. Anal. 19 (1988), 1455-1461.