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Hello,

I've to calculate the derivate of :

[tex]

\displaystyle \sigma_{N}(t):=\sum_{i=1}^{N}g_{i}(t)

[/tex]

and [tex] g_{i}(t) [/tex] verify the differential equation:

[tex] \displaystyle \frac{d g_i}{d t}(t) =

\sum_{k=1}^{i-1} \frac{1}{k}K(k,i-k) g_{i-k}(t) g_k(t) - \sum_{l=1}^{\infty} \frac{1}{l}K(l,i) g_i(t)g_l(t) [/tex].

I've to justify:

[tex] \displaystyle \partial_{t}\sigma_{N}(t):= - \sum_{i,j\leqN;i+j>N}\frac{1}{j}K(j,i) g_i(t)g_l(t) [/tex]

Thanks.

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# Partial diff eq

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