Can anyone prove that

[tex] \langle r \rangle = \langle nlm|r|nlm\rangle = \frac{a}{2}(3 n^2-l(l+1))[/tex].

Where a - bohr radious.

I've been trying to prove it using some property of Laguerre polynomials (which are

radial part of eigenstates) but I stucked in it.

I found this equation in "Princliples of QM" by Shankar

(unfortunately with neither proof nor hint).