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The Hermite polynomials can be defined through

[tex]\displaystyle{F(x,h) = \sum^{\infty}_{n = 0} \frac{h^n}{n!}H_n(x)}[/tex]

Prove that the [tex]H_n[/tex] satisfy the hermite equation

[tex]\displaystyle{H''_n(x) - 2xH'_n(x) + 2nH_n(x) = 0}[/tex]

Using

[tex]\displaystyle{\sum^{\infty}_{n = 0} \frac{h^n}{n!}nH_n(x) = h\frac{\partial}{\partial h}F(x,h)}[/tex]

Can someone give me a bit of a push in the right direction?