Chapter 2.3, Problem 2.16P

(a)

To determine

The derivation for $H_3$ and $H_4$ by Rodrigues formula.

(b)

To determine

The expression for $H_5$ and $H_6$ using Hermite polynomial.

(c)

To determine

The check for expression $\frac{d{H}_n}{d\text{ξ}}=2n{H}_{n-1}\left(\text{ξ}\right)$.

(d)

To determine

The expression for $H_1$, $H_2$ and $H_3$.