something I don't understand to do with Dirichlets theorem
Hi,
the following is something I've been reading.
He started from the power series
\(\sum_{n=1}^\infty \big(\frac{n}{q}\big)x^n=\frac{1}{1x^q}\sum_{m=1}^{q1}\big(\frac{m}{q}\big)x^m=\frac{xf(x)}{1x^q}\)
say, and by putting this in the formula
\(\Gamma(s)n^{1}=\int_0^1 x^{n1}(\log x^{1})^{s1} \mathrm{d}x\)
he obtained
\(\Gamma(s)L(s)=\int_0^1\frac{f(x)}{x^q1}(\log x^{1})^{s1}\mathrm{d}x\)
I'm stuck because I can't see how he put what he put in the formula.
Can anyone explain it step by step?
Last fiddled with by wildrabbitt on 20200223 at 17:32
