Asymptotic Analysis of a Family of Polynomials Associated with the Inverse Error Function
PublisherRocky Mountain Mathematics Consortium
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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.
CitationDominici D, Knessl C. ASYMPTOTIC ANALYSIS OF A FAMILY OF POLYNOMIALS ASSOCIATED WITH THE INVERSE ERROR FUNCTION. Rocky Mountain Journal of Mathematics. 2012;42(3):847-872. DOI: 10.1216/RMJ-2012-42-3-847
SubjectInverse error function
discrete WKB method