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.

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