Legendre polynomials

1. Jan 5, 2012

Elliptic

1. The problem statement, all variables and given/known data
Integrate the expression
Pl and Pm are Legendre polynomials

2. Relevant equations

3. The attempt at a solution
Suppose that solution is equal to zero.

File size:
1.8 KB
Views:
93
2. Jan 5, 2012

TheFurryGoat

What properties do you know about Legendre Polynomials? If you can use the orthogonal properties that are listed in the article on Legendre polynomials in wikipedia, then integration by parts should do the trick.

3. Jan 5, 2012

Elliptic

But, how make Pm'(x) I don't understand(recurrent differentiation formula?)

4. Jan 5, 2012

TheFurryGoat

Under the orthogonality section in the wikipedia article on Legendre polynomials, you find the identity
$\displaystyle \frac{d}{dx}\left[(1-x^2)\frac{d}{dx}P(x)\right] = -\lambda P(x)$
where the eigenvalue $\lambda$ corresponds to $n(n+1).$
I suppose $P(x)=P_n(x)$ for any $n$, but I'm not sure though. If this is the case, and you know this property, then integration by parts should do the trick.

5. Jan 6, 2012

Elliptic

Thanks for help, I succeeded to do job.