From the definition given by wikipedia and Cauchy's theorem i can find the branch points of $\arcsin$ through its derivative $\displaystyle\frac{1}{\sqrt{1-x^2}}$
Are -1 and 1 simple pole of this expression ? (i'm a bit confused because of the fractional power)
Also, there is also a branch point at infinity. How do i find this branch point ? what are the order of all the branch points of arcsin ?
From wikipedia, i know that simple pole of derivative means logarithmic branch point, so there is no order if -1 and 1 are simple pole of $\displaystyle\frac{1}{\sqrt{1-x^2}}$ ?