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Displaying similar documents to “Zhedanov's algebra A W ( 3 ) and the double affine Hecke algebra in the rank one case. II. The spherical subalgebra.”

Linearization of the product of orthogonal polynomials of a discrete variable

Saïd Belmehdi, Stanisław Lewanowicz, André Ronveaux (1997)

Applicationes Mathematicae

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Let P k be any sequence of classical orthogonal polynomials of a discrete variable. We give explicitly a recurrence relation (in k) for the coefficients in P i P j = k c ( i , j , k ) P k , in terms of the coefficients σ and τ of the Pearson equation satisfied by the weight function ϱ, and the coefficients of the three-term recurrence relation and of two structure relations obeyed by P k .