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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.