Legendre Polynomials - expansion of an isotropic function on a sphere

[petmal]

Hello.
I don't know what to do with one integral. I am sure it is something very simple, but I just don't see it...

For some reason I am not able to post the equations, so I am attaching them as a separatre file.

Many thanks for help.

 

[mathman]

Something is missing. It looks like the integration will give you an identity C_l=C_l.

 

[petmal]

Something is missing. It looks like the integration will give you an identity C_l=C_l.

Well, I want to get C_{l}, right? That is why I apply P_{l} on the correlation function (1) and integrate - it removes P_{l} and the sum leaving C_{l} * some factor in l. Where do you see a mistake?

Thanks.