Geodesic
A Combinatorial Interpretation of the Integral of the Product of Legendre Polynomials
Séminaire lotharingien de combinatoire, 14s (1986) 
Joe Gillis; J. Jedwab an Doron Zeilberger. A Combinatorial Interpretation of the Integral of the Product of Legendre Polynomials. Séminaire lotharingien de combinatoire, 14s (1986). http://geodesic.mathdoc.fr/item/SLC_1986_14s_a2/
@article{SLC_1986_14s_a2,
     author = {Joe Gillis and J. Jedwab an Doron Zeilberger},
     title = {A {Combinatorial} {Interpretation} of the {Integral} of the {Product} of {Legendre} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1986},
     volume = {14s},
     url = {http://geodesic.mathdoc.fr/item/SLC_1986_14s_a2/}
}
TY  - JOUR
AU  - Joe Gillis
AU  - J. Jedwab an Doron Zeilberger
TI  - A Combinatorial Interpretation of the Integral of the Product of Legendre Polynomials
JO  - Séminaire lotharingien de combinatoire
PY  - 1986
VL  - 14s
UR  - http://geodesic.mathdoc.fr/item/SLC_1986_14s_a2/
ID  - SLC_1986_14s_a2
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%0 Journal Article
%A Joe Gillis
%A J. Jedwab an Doron Zeilberger
%T A Combinatorial Interpretation of the Integral of the Product of Legendre Polynomials
%J Séminaire lotharingien de combinatoire
%D 1986
%V 14s
%U http://geodesic.mathdoc.fr/item/SLC_1986_14s_a2/
%F SLC_1986_14s_a2

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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.