Around any point a with |a|>1.
As far as I know, the principal nth root of z is defined as \sqrt[n]{|z|}e^{\frac{1}{n}i\mathrm{Arg}z}, which doesn't seem very helpful; how would you expand \sqrt{z} around a point where it is defined?
Perhaps these are silly questions; my book is very vague on...
How do I find the Laurent expansion of a function containing the principal branch cut of the nth root?
Example:
f(z)=-iz\cdot\sqrt[4]{1-\frac{1}{z^{4}}}
I'm stuck trying to prove a step inside a lemma from Serre; given is
0<a<b
0<x
To prove:
|\int_{a}^{b}e^{-tx}e^{-tiy}dt|\leq\int_{a}^{b}e^{-tx}dt
I've tried using Cauchy-Schwartz for integrals, but this step is too big (using Mathematica, it lead to a contradiction); something...