Séminaire Lotharingien de Combinatoire, B16a (1988), 14pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1987/S-16, p. 73-86.]

Dominique Foata and Doron Zeilberger

Linearization coefficients for the Jacobi polynomials

Abstract. The explicit non-negative representation of the linearization coefficients of the Jacobi polynomials obtained by Rahman seems to be difficult to be derived by combinatorial methods. However several combinatorial interpretations can be provided for the integral of the product of Jacobi polynomials and furnish an evaluation of this integral in the particular case where the subscript of the first polynomial is equal to the sum of the subscripts of the other polynomials.

foata@math.u-strasbg.fr, zeilberg@euclid.math.temple.edu

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