Transverse limits in the Askey tableau
Limit relations between classical discrete orthogonal polynomials (Charlier, Meixner, Krawtchouk, Hahn) to classical continuous orthogonal polynomials (Jacobi, Laguerre, Hermite) -- so-called tranverse limits -- can be described by relations of type \(\lim_{\omega\rightarrow 0}P_n(x(s,\omega))=Q_n(s)\) where \(P_n(x)\) and \(Q_n(x)\) correspond to the discrete and continuous family, respectively. The authors consider the expansions \(P_n(x(s,\omega))=\sum_{k=0}^\infty R_k(s;n)\omega^k\), and develop a method to compute the coefficients \(R_k(s;n)\) by using certain connection and inversion coefficients.
scientific article; zbMATH DE number 1326392
scientific article