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Does anyone know of any clever tricks that solve

$$\large G_n(t) = \int_0^t dt_1 \int_0^{t_1} dt_2 \cdots \int_0^{t_{n-2}}dt_{n-1}\int_0^{t_{n-1}}dt_{n} e^{i\lambda(t_1-t_2+t_3-\cdots + t_{n-1}-t_n)}$$

I've come up with a few recursion relations but I'm finding it hard to pin down the exact answer.

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    You can separate the exponential. Why don't you do that?2012-03-07
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    That doesn't help much. If you separate and then evaluate the first integral you wind up with $-\frac{1}{i\lambda}\left(e^{-i\lambda t_{n-1}} - 1\right)$. The exponent term will cancel the exponent in the next integral, which will produce ultimately polynomial terms in $t$. I didn't make too much progress with that approach.2012-03-07
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    I get the recursion $$G_n(t) = \frac{t_{n-2} G_{n-2} - G_{n-1}}{i\lambda (-1)^{n+1}}$$ which doesn't seem to yield a nice answer unless there is some relation between the $t_i$'s.2012-03-07
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    If the bounds in the inner integrals didn't depend on the varaibles with respect to which one integrates in the outer integrals, then "separating" the exponential would pay off. But it's less clear that it will in the present situation.2012-03-07
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    @fatbox May I ask where does such an integral arise?2012-03-08

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