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2020-02-24, 12:49   #6
Dr Sardonicus

Feb 2017
Nowhere

17·263 Posts

Quote:
 Originally Posted by wildrabbitt I just wrote what was written in the book. I'm pretty sure it's supposed to be $$\log \frac{1}{x}$$ otherwise it would have been written the way you wrote.
Ah, log(1/x), not 1/log(x). OK, now I see a Gamma-function integral in prospect in your second equation. (x = exp-u, scribble scribble, u = t/n, scribble scribble...)

Your second equation is wrong. It should be

$\Gamma(s)n^{-s}=\int_0^1 x^{n-1}(\log x^{-1})^{s-1} \mathrm{d}x$

(It is n-s on the left side, not n-1)