Editing Hermite polynomials (section)

===Special values===
The physicist's Hermite polynomials evaluated at zero argument {{math|''H<sub>n</sub>''(0)}} are called [[Hermite number]]s.

<math display="block">H_n(0) = \begin{cases} 
 0 & \text{for odd }n, \\
 (-2)^\frac{n}{2} (n-1)!! & \text{for even }n,
\end{cases}</math>
which satisfy the recursion relation {{math|1=''H<sub>n</sub>''(0) = −2(''n'' − 1)''H''<sub>''n'' − 2</sub>(0)}}. Equivalently, <math>H_{2n}(0) = (-2)^n (2n-1)!!</math>.

In terms of the probabilist's polynomials this translates to
<math display="block">\operatorname{He}_n(0) = \begin{cases} 
 0 & \text{for odd }n, \\
 (-1)^\frac{n}{2} (n-1)!! & \text{for even }n.
\end{cases}</math>