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I think q is changing, since the work is done to change E.

$$W = U = \frac{q^2}{2C} =\frac{q q d}{2 \kappa \epsilon_0 A} = \frac{E P}{2}$$ Then , since E is constant we have that : $$\delta W = \frac{dW}{dP} dP = \frac{E}{2} dP$$. My question is how can I make this 2 on the denominator disappear in order to obtain the required expression ? ps : In...

Thank you very much! I think I got it now

This is exercise 12.1.2 a from Arfken's Mathematical Methods for Physicists 7th edition :Starting from the Laguerre ODE, $$xy''+(1-x)y'+\lambda y =0$$ obtain the Rodrigues formula for its polynomial solutions $$L_n (x)$$ According to Arfken (equation 12.9 ,chapter 12) the Rodrigues formula...

Thank you very much for the explanation !