This article is about doubly infinite power series. For power series with finitely many negative exponents, see Formal Laurent series.
A Laurent series is defined with respect to a particular point and a path of integration γ. The path of integration must lie in an annulus, indicated here by the red color, inside which is holomorphic (analytic).
In mathematics, the Laurent series of a complex function is a representation of that function as a power series which includes terms of negative degree. It may be used to express complex functions in cases where a Taylor series expansion cannot be applied. The Laurent series was named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass had previously described it in a paper written in 1841 but not published until 1894.[1]