The problem here is to compute $$\int_0^\infty \log(1+tx)t^{p1}dt$$ where $p\in(0,1)$ and $x>0$. This is a great problem for contour integration. Just tricky enough to be really interesting. What makes it interesting is that there are two functions in the integrand needing their own separate branch cuts. One must keep in mind that each function only […]

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