Linearization of the product of orthogonal polynomials of a discrete variable

Volume 24 / 1997

Saïd Belmehdi, Stanisław Lewanowicz, André Ronveaux Applicationes Mathematicae 24 (1997), 445-455 DOI: 10.4064/am-24-4-445-455

Abstract

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 $P_iP_j=\sum_kc(i,j,k)P_k$, 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 {$P_k$}.

Authors

  • Saïd Belmehdi
  • Stanisław Lewanowicz
  • André Ronveaux

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