Originally Posted by

**garunas** Using the identity:

$\displaystyle \sum_{n=0}^\infty P_{n}(x)r^n = \frac{1}{\sqrt {1-2xr+r^2} }$ with:

$\displaystyle x \in [-1,1], r \in (-1,1)$

Derive an expression for $\displaystyle P_{2}(x)$ the legendre polynomial of degree 2.

Any help here will be amazing as I absolutely haven't got a clue!

Also from this it also asks to evaluate $\displaystyle P_{3}'(0)$ but i take that if you can find $\displaystyle P_{2}(x)$ then you can also find $\displaystyle P_{2}'(0)$ and use the same method for $\displaystyle P_{3}(x)$

Thank you