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Hermite Polynomials
Definition
The Hermite polynomials are defined as
\[
\begin{align}
H_n(x) &= n! \sum_{k=0}^{[n/2]} \frac{(-1)^k}{k!(n-2k)!} (2x)^{n-2k}\\
&= (2x)^n {}_2F_0 \left(\left. {-n/2, -(n-1)/2 \atop -} \; \right| -\frac{1}{x^2} \right)
\end{align}
\]
