Rodrigues’ formula of Laguerre

[jije1112]

Homework Statement

I need to proof that Rodrigues’ formula satisfies Laguerre differential equation

Homework Equations

Rodrigues’ formula of Laguerre

Laguerre differential equation

The Attempt at a Solution

first,I have to calculate

=

I tried to sum both terms and this is what I got

after that I did not know what to do (what this differentiation should be)

 

[Buzz Bloom]

Hi jije:

I would suggest proof by induction.

First prove for n = 0. Then show that if true for n, it is also true for n+1.

Hope this helps.

Regards,
Buzz