posted on 21.10.2013, 00:00by Diego Dominici, Charles Knessl
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.
The work of the first author was supported by a Humboldt Research Fellowship
for Experienced Researchers from the Alexander von Humboldt Foundation. The
work of the second author was supported by NSF grant DMS 05-03745 and NSA
grants H 98230-08-1-0102 and H 98230-11-1-0184.
The original version is available through Rocky Mountain Mathematics Consortium at DOI: 10.1216/RMJ-2012-42-3-847.
Dominici 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