Recurrence relations for the connection coefficients of orthogonal polynomials of a discrete variable on the lattice \(x(s)=q^{2s}\)
Let \(\{P_k(x)\}\) be any system of classical orthogonal polynomials of a discrete variable such that \[ \sum^{B-1}_0 P_k(x(s)) P_\ell(x(s)) \ell(s)\Delta x(s-1/2)= \delta_{k\ell} d^2_k \] and also \(\overline P_n= \sum^n_0 C_{nk}P_k\), where \(\overline P_n\) is another family of similar polynomials and \(C_{nk}\) are connection coefficients. In this paper the recurrence relations satisfied by the connection coefficient in terms of the coefficients \(\sigma\) and \(\tau\) of the Pearson equation, have been obtained.
scientific article; zbMATH DE number 1326373