Frobenius method for hermite's differential equation

Hello

I am working on a problem but have found myself stuck and confused as to how t continue...

Thr problem is... Using frobenius mood, seek a solution of Hermite's differential equation

d^{2}y/dx^{2 }-2x dy/dx +2my =0 In the form of a power series

Y(x)= (n=0 n= inf) a_{n} x^{x+r }A_{0 }=/= 0

Im new to this and not very good with the notation...

I have then found y(x), y'(x) and y''(x) and substitute them into the differential equation it is then I can't work out how t rearrange and Solve... Please helppp!!!

Re: Frobenius method for hermite's differential equation

First there is a good tutorial for "LaTex" formatting that is used on this board. Just start with "[ tex ]" and end with "[/ tex ]" (without the spaces):Introducing LaTeX Math Typesetting

Please show what you **have** done. What did you get when you differentiated and put y, y', and y'' into the equation?

(You don't really need the "+r" in the exponent because this not really a Frobenious equation- the leading coefficient is never 0 so it is sufficient to look for a solution of the form $\displaystyle \sum_{n=0}^\infty a_nx^n$)

Re: Frobenius method for hermite's differential equation

The question is a past exam question from a previous year.. It contains the +r so I'm not sure if I would actually have to include it....

So far I have.....

\sum_{n=0}^\infty (n+r-1) a_nx^(n+r-2) - 2 \sum_{n=0}^\infty (n+r) a_nx^(n+r) +2m \sum_{n=0}^\infty a_nx^(n+r)

But its from this I'm stuck what to do next.....