Quote:
Originally Posted by wildrabbitt
Hi,
the following is something I've been reading.
He started from the power series
x^n=\frac{1}{1-x^q}\sum_{m=1}^{q-1}\big(\frac{m}{q}\big)x^m=\frac{xf(x)}{1-x^q}\))
say, and by putting this in the formula
n^{-1}=\int_0^1 x^{n-1}(\log x^{-1})^{s-1} \mathrm{d}x\))
he obtained
L(s)=-\int_0^1\frac{f(x)}{x^q-1}(\log x^{-1})^{s-1}\mathrm{d}x\))
I'm stuck because I can't see how he put what he put in the formula.
Can anyone explain it step by step? |
I took the liberty of TEXing your equations. That makes them a whole lot easier to read, for me at least. You can probably drop the big parens.
Is that supposed to be (log(x)
-1^(s-1)? That would be log(x)
1-s, yes?