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Let $\omega_i$, $i=1,\dots,n$ be positive real numbers. Consider the following nested integral $$ \int_0^{t} \cos(\omega_1t_1)\left(\int_0^{t_1} \cos(\omega_2t_2)\cdots \left(\int_0^{t_{n-1}} \cos(\omega_nt_n)\, \mathrm{d}t_n\right)\cdots\mathrm{d}t_2\right) \mathrm{d}t_1 $$

Q. Does there exist a closed-form expression for the latter integral? If not, is it possible to say that the latter integral is bounded in $t$?

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  • $\begingroup$ For $n=2$, it is quite simple. For $n=3$, it is doable but quite nasty. $\endgroup$ – Claude Leibovici May 19 '18 at 5:44
  • $\begingroup$ @ClaudeLeibovici: So, do you think there isn't any chance to find a closed-form expression (or, at least, a tractable bound)? $\endgroup$ – Ludwig May 19 '18 at 19:03

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