Talk:Laurent series

I wonder if it is useful to allow for infinitely many negative-exponent terms, so that functions with essential singularities can be described? You can't talk formally about those of course. AxelBoldt, Thursday, July 11, 2002

The problem is that if you allow for infinitely many negative-exponent terms, Laurent series stop being unique. For instance:

1 + 1/x + 1/x² + 1/x³ + ... = 1/(1 - 1/x) = -x/(1 - x) = -x(1 + x + x² + x³ + ...) = -x - x² - x³ - x⁴ - ...