How do we find asymptotic behavior of Hermite polynomials? I tried to check, but i can only find the final expression but not the method.
2026-03-28 09:55:29.1774691729
How to find asymptotic behaviour?
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You can prove by induction that the $n$th derivative of $e^{-x^2/2}$ is $e^{-x^2/2}$ multiplied by a polynomial of degree of $n$ with leading factor $(-1)^n$, hence the (probabalist's) Hermite polynomials all have leading factor $1$, and so tend to positive infinity asymptotically.