Does a Laurent series expansion exist?...

Prove [or even disprove...] that the principal branch of the function http://www.mathhelpforum.com/math-he...c90f838de7.png cannot be expanded in Laurent series around the point http://www.mathhelpforum.com/math-he...916cba57f4.png , i.e. a coefficient set http://www.mathhelpforum.com/math-he...cdc2c8e98a.png such that for a definite region of the complex plane which is not limited to only one point is...

http://www.mathhelpforum.com/math-he...049e8378a4.png (1)

... doesn't exist.

Kind regards