CAOP

Plot

Hermite Polynomials

Definition

The Hermite polynomials are defined as

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

Differential Equation

Recurrence Equation

Parameters

Variables

\(n\)

\(x\)

factor (use Maple-style input)

   hypergeometric term in \(n\) and hyperexponential term in \(x\) required