Is a limit point of branch points a branch point?
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I have come into a discussion with my friends over a complex analysis question: Is $infty$ a branch point of $log(cos z)$ ? I can't get a clear answer to this from the definition of branch points. Maybe it's because I've only learnt about primary complex analysis which defines branch point as 'a point which, if you run $z$ through any contour around it, would change the value of $f(z)$ '. Since $frac{pi}{2}+npi ,forall n in mathbb{Z}$ are branch points of $f(z)=log(cos z)$ , $infty$ is a limit point of branch points. Follow the above definition, it seems that any contour around $infty$ would change the value of $f(z)$ , but it also seems that this should be the credit of the finite branch points. So, based on rigid definitions, is $infty$ a branch point of $f(z)=log(co
