hermite

hermite (n, x)

The hermite function returns the Hermite polynomial of order n :

\displaystyle H_{n}(x)=(-1)^{n} \exp \left(x^{2}\right) \frac{d^{n}}{d x^{n}} \exp \left(-x^{2}\right) .

The first few polynomials are:

\displaystyle \begin{array}{l} 1 \\ \\ 2 x \\ \\ 4 x^{2}-2 \\ \\ 8 x^{3}-12 x \end{array}