Recent problems from uniform asymptotic analysis of integral in particular in connection with Tricomi's Psi Psi -function

The paper discusses asymptotic methods for integrals, in particular uniform approximations. We discuss several examples, where we apply the results to Tricomi's $Psi-$function, in particular we consider an expansion of Tricomi-Carlitz polynomials in terms of Hermite polynomials. We mention other recent expansions for orthogonal polynomials that do not satisfy a differential equation, and for which methods based on integral representations produce powerful uniform asymptotic expansions

Research fellowship for Dr. E.M. Harrell

Issued as Memorandums [nos. 1-2], and Project abstracts [nos. 1-6], Project no. G-37-60