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More on the log sine integral $\int_0^{\pi }\theta ^{3}\log^{3}\left ( 2\sin\frac{\theta }{2} \right )\mathrm{d}\theta$
I. In this post, the OP asks about the particular log sine integral,
$$\mathrm{Ls}_{7}^{\left ( 3 \right )} =-\int_{0}^{\pi }\theta ^{3}\log^{3}\left ( 2\sin\frac{\theta }{2} \right )\,\mathrm{d}\...
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How to solve this summation (Lerch Transcendent)?
How is it possible to deduce the closed form of the following?
$$\sum_{i = 0}^{n - 1} \frac{2^i}{n - i} = ?$$
