Normalisation of associated Laguerre polynomials

1. Nov 7, 2008

bdforbes

I'm looking right now at what purports to be the normalisation condition for the associated Laguerre polynomials:

$$\int_0^\infty e^{-x}x^k L_n^k(x)L_m^k(x)dx=\frac{(n+k)!}{n!}\delta_{mn}$$

However, in the context of Schroedinger's equation in spherical coordinates, I find that my normalisation integral has a different form:

$$|N|^2\int_0^\infty (\alpha r)^l e^{-\alpha r}[L_{n-l-1}^{2l+1}(\alpha r)]^2 r^2 dr=1$$

I understand that I can evaluate this integral using the generating function of the associated Laguerre polynomials, but I'm a bit confused about why there are two forms for normalisation. Can anyone shed any light on this? Thanks.

2. Dec 8, 2008

Shredinger

hey still need help on that?

3. Dec 8, 2008

bdforbes

No thanks I figured it out.