Asymptotic Analysis of a Family of Polynomials Associated with the Inverse Error Function

We analyze the sequence of polynomials defined by the differential-difference equation Pn+1(x) = P'(n)(x)+x(n+1)P-n(x) asymptotically as n -> infinity. The polynomials P-n(x) arise in the computation of higher derivatives of the inverse error function inverf (x). We use singularity analysis and discrete versions of the WKB and ray methods and give numerical results showing the accuracy of our formulas.