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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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