Transverse limits in the Askey tableau

Limit relations between classical discrete (Charlier, Meixner, Kravchuk, Hahn) to classical continuous (Jacobi, Laguerre, Hermite) orthogonal polynomials (to be called transverse limits) are nicely presented in the Askey tableau and can be described by relations of type limω→0 Pn(x(s, ω)) = Qn(s), where Pn(s) and Qn(s) stand for the discrete and continuous family, respectively. Deeper information on these limiting processes can be obtained by expanding the discrete polynomial family as Pn(x9s, ω)) = ∑k=0∞ωkRk(s; n). In this paper a method for computing the coefficients Rk(s; n) is designed the main tool being the consideration of some closely related connection and inversion problems.