Work out the normalization factor for the spherical harmonics, as follows. From section...

Work out the normalization factor for the spherical harmonics, as follows. From section 4.12 we know that

The problem is to determine the factor (which I quoted, but did not derive, in Equation 4.32). use Equations 4.120, 4.121, and 4.130 to obtain a recursion relation giving in terms of solve it by induction on m to get up to an overall constant, Finally, use the result of Problem 4.22 to fix the constant. You may find the following formula for the derivative of an associated Legendrefunction useful: