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Licensed Unlicensed Requires Authentication Published by Oldenbourg Wissenschaftsverlag September 25, 2009

Asymptotic analysis of generalized Hermite polynomials

  • Diego Dominici
From the journal Analysis

We analyze the polynomials Hnr(x) considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of Hnr(x) and derive asymptotic approximations for large values of n from their differential-difference equation, using a discrete ray method. We give numerical examples showing the accuracy of our formulas.

Received: 2007-January-01
Revised: 2007-October-24
Published Online: 2009-09-25
Published in Print: 2008-02

© Oldenbourg Wissenschaftsverlag

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