This is a second paper on finite exact representations of certain polynomials in terms of Hermite polynomials. The representations have asymptotic properties and include new limits of the polynomials, again in terms of Hermite polynomials. This time we consider the generalized Bernoulli, Euler, Bessel and Buchholz polynomials. The asymptotic approximations of these polynomials are valid for large values of a certain parameter. The representations and limits include information on the zero distribution of the polynomials. Graphs are given that indicate the accuracy of the first term approximations.

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (msc 33C45), Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (msc 41A60), Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) (msc 30C15), Approximation by polynomials (msc 41A10)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

López, J.L, & Temme, N.M. (1999). Hermite polynomials in asymptotic representations of generalized Bernoulli,Euler, Bessel and Buchholz polynomials. Modelling, Analysis and Simulation [MAS]. CWI.