I am trying to make a nested integral operator where the output function of one step must be applied to the dummy variable to be integrated in the next step. Here my code:
w[x_] := Cos[x];
f[t_, n_] := Nest[Integrate[w[t - s] #, {s, 0, t}] &, 1, n];
Observe that, in one step, the output function is applied in $t$ and not $s$. Therefore, in the next integration, $t$ is just a constant, but it must be integrated as well. How can I fix this?
f[0, t_] := 1; f[n_Integer?Positive, t_] := Integrate[Cos[t - s] f[n - 1, s], {s, 0, t}]. The more efficient method involves using the method in this answer. – J. M.'s missing motivation Nov 09 '17 at 01:06#to((#) /. t -> s)infget you what you need? – Edmund Nov 09 '17 at 01:15