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Asymptotic analysis of generalized Hermite polynomials

Diego Dominici
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Abstract

We analyze the polynomials $H_{n}^{r}(x)$ considered by Gould and Hopper, which generalize the classical Hermite polynomials. We present the main properties of $H_{n}^{r}(x)$ 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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Diego Dominici. 2006-06-14. Asymptotic analysis of generalized Hermite polynomials. https://arxiv.org/abs/math/0606324

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