A question on the orthogonal polynomial

[sufive]

Dear All Friends,

I am currently working on a project which needs some orthogonality
integration formulae of Laguerre polynomials. I referred worlfram's math
function site
http://functions.wolfram.com/Polynomials/LaguerreL3/21/02/01/
and get three seemingly useful ones.

However, as very natural exercises, when I made tests by setting
(p=1,alpha=lambda+1,beta=lambda,m=n) in the third equation of the
above web-page and try to get the first one, I always cannot accomplish
the goal. So I suspect the inter-consistances of the three integration formulae
in the above web-page.

Is here someone professional in orthogonality polynomials and would like
to resolve my suspicious? Or can here someone recommend me some
materials so that I can learn and derive out the desired integration formulae
by myself?

Thank you very much!

 

[susskind_leon]

Check out Dixon's identity and the rules for the Gamma function (basically that it's just factorial for integer arguments) and you will find your way from eq.3 to eq.1

 

[sufive]

Thank you very much! I worked it out just as you suggested!