I have a simple double sum as function:
u[m_, n_] = Sum[m^M/M! * n^N/N!, {M, 0, Infinity}, {N, 0, M - 1}]
and would like to compute the partial derivatives.
D[u[m, n], m]
I can't get the output neatly here, but it basically gives me (with correct indices on the summations)
$$ \left(\sum \sum \frac{m^{M-1}M n^N}{M! N!}\right)[m, n] + \left(\sum \sum \frac{m^{M} n^N}{M! N!}\right)^{(1, 0)}[m, n]$$
I would have thought that the first term would be the correct answer. I looked up the $(1, 0)$ notation and it apparently means "partial derivative w.r.t. the first input" - but isn't that exactly what I've put in here?
How am I supposed to understand this result?
N
since it is a built-in function. $\endgroup$