Feynman
Jul7-04, 03:07 AM
:mad:
:surprise:
Hello,
I've to calculate the derivate of :
\displaystyle \sigma_{N}(t):=\sum_{i=1}^{N}g_{i}(t)
and g_{i}(t) verify the differential equation:
\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) .
I've to justify:
\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)
Thanks.
:surprise:
Hello,
I've to calculate the derivate of :
\displaystyle \sigma_{N}(t):=\sum_{i=1}^{N}g_{i}(t)
and g_{i}(t) verify the differential equation:
\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) .
I've to justify:
\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)
Thanks.