# Legendre Series Expansion

1. Mar 4, 2014

### Axis001

1. The problem statement, all variables and given/known data

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

2. Relevant equations

(n+1)Pn+1 + nPn-1 = (2n+1)xPn

ƒn = $\sum$ CnPn(x)

Cn = $\int$ f(x)*Pn(u)

3. The attempt at a solution

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

$\int$ (n+1)Pn+1(x)dxPn(x)

and

$\int$ nPn-1(x)dxPn(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.

Last edited: Mar 4, 2014
2. Mar 12, 2014

### Dustinsfl

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