Asymptotic analysis of generalized Hermite polynomials
Diego Dominici
Abstract
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.
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