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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!