# Expanding in powers of 1/z (Laurent series)

by Harudoz
Tags: 1 or z, expanding, laurent, powers, series
 Emeritus Sci Advisor PF Gold P: 4,500 Is this a complex analysis course, or is it something that had complex analysis as a prerequisite? Practically, to calculate these you can often do standard Taylor series calculations $$f(x)=\frac{x}{1-x} = \frac{1}{1-1/x}$$ we know how to expand 1/(1-1/x) using the Taylor series for 1/(1-x) $$f(x) = 1+\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+...$$ and this is valid as long as |x|>1