Uniform asymptotic expansions
With this tutorial lecture the author aims at illustrating two extensions of the steepest descent method. First, the method of Chester, Friedman and Ursell, handling the coalescence of two saddle points at a single point, is discussed, along with the derivation of the uniform asymptotics for Hermite polynomials \(H_n(\sqrt{2n+1} t)\). Next, an extension of this approach allowing to compute uniform asymptotic expansions when two saddle points coalesce at two different locations is presented, and applied to the study of the asymptotic behavior of the zeros of Meixner-Pollaczek polynomials.NEWLINENEWLINEFor the entire collection see [Zbl 0969.00053].
scientific article; zbMATH DE number 1684169