I'm doing a project actually and I have a small problem to demonstrate an equality.
Using Laguerre polynomials $L_p(t)$ (with p the order of the polynomial), we define $\phi_p$(t) = $\exp(-t/2)$* $L_p(t)$.
Assuming $V(t)$ = $\sum \limits_{p=0}^{m-1}$ $V^p$$\phi_p(t)$
The equation is: $\frac{\partial V(t)}{\partial t}$ = $\sum \limits_{p=0}^{m-1}(\frac{1}{2}$ $V^p$ + $\sum \limits_{j=0}^{p-1}$ $V^j$)$\phi_p(t)$
I have no problem for the first term, but I don't really understand how to obtain the term $\sum \limits_{j=0}^{p-1}$ $V^j$.
If someone has an idea, it would be very helpful !
Thank you in advance
Stephane