Showing a limited preview of this publication:
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.
Keywords: Hermite polynomials; asymptotic analysis; ray method; differential-difference equations; discrete WKB method
Received: 2007-January-01
Revised: 2007-October-24
Published Online: 2009-09-25
Published in Print: 2008-02
© Oldenbourg Wissenschaftsverlag