A problem while verifying the generating function of Legendre Polynomials.

[LeLou]

Our professor gave us an a problem to solve, she asked us to prove or verify the following identity:

http://img818.imageshack.us/img818/5082/6254.png

Where $\Phi$ is the Generating function of Legendre polynomials given by:

$\Phi$_(x,h)= (1 - 2hx + h²)^-1/2


2. This Identity is from (Mathematical Methods in The Physical Sciences, Mary L.Boas, page 491)


She told us to start By solving the last term & then plug in the first two terms. I have differentiated the function so many times, failed to at least verfy that the identity really equals zero.

 

[vela]

You must be making a mistake differentiating or in the algebra, but we can't help you find it if you don't show your work.

 

[Mindscrape]

Also, I remember some of the Legendre proofs involve recursive relationships. I don't think this is one of them, but it may be (I haven't worked out since this is your HW).