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

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journal contribution
posted on 21.10.2013 by 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.

Funding

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.

History

Publisher Statement

The original version is available through Rocky Mountain Mathematics Consortium at DOI: 10.1216/RMJ-2012-42-3-847.

Citation

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

Publisher

Rocky Mountain Mathematics Consortium

Language

en_US

issn

0035-7596

Issue date

01/01/2012

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