How do I find the n+1 and n-1 order expansion of a Legendre series?

[Axis001]

Homework Statement

Find the n+1 and n-1 order expansion of \stackrel{df}{dy}

Homework Equations

(n+1)P_n+1 + nP_n-1 = (2n+1)xP_n

ƒ_n = \sum C_nP_n(x)

C_n = \int f(x)*P_n(u)

The Attempt at a Solution

I know you can use the recursion relation for Legendre Polynomials once you combine C_n with the summation to get two terms one for f_n+1 and one for f_n-1.

\int (n+1)P_n+1(x)dxP_n(x)

and

\int nP_n-1(x)dxP_n(x)

At this step I'm not exactly sure as what to do. I don't use Legendre Series very often so I tend to get confused by them. Do you just use the simple 2/(2n+1) solution from the orthogonality property and use n = n+1 or n = n-1?

Thanks for any help in advance.

 

[Dustinsfl]

I don't understand your question. Can you clarify it?