# 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.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook