Im stuck on this question :((adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Hermite Polynomials

**Physics Forums | Science Articles, Homework Help, Discussion**