Volume Integral Orthogonal Polynomials

[VVS]

Hello.

Homework Statement

Basically I want to evaluate the integral as shown in this document:
View attachment integral.pdf

Homework Equations

The Attempt at a Solution

The integral with the complex exponentials yields a Kronecker Delta.
My question is whether this Delta can be taken inside the integral over phi space?

 

[BvU]

I think so. That is to say you can simply replace p by m and forget about $\theta$.
Check for a possible constant factor in case you want to look at orthonormality. For orthogonality you don't have to bother.

 

[VVS]

Thanks