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So, does the Laurent series of an analytic function f allow convergence outside of the RoC for the normal power series of f?--[[User:Rgilhamw|Rgilhamw]] 19:50, 25 November 2009 (UTC) | So, does the Laurent series of an analytic function f allow convergence outside of the RoC for the normal power series of f?--[[User:Rgilhamw|Rgilhamw]] 19:50, 25 November 2009 (UTC) | ||
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| + | I don't think so. It seems like the laurent series is just another power series representation of the function with another ROC. Like the example in the book 1/(1-z) can be represented by a power series with negative powers of z but with ROC abs(z)>1 instead of less than 1. The Laurent series seems like it is used to represent an analytic function in the annulus <math> r<z-c<R </math> where c is the center of the annulus.< --[[User:Apdelanc|Adrian Delancy]] | ||
Revision as of 12:35, 28 November 2009
Homework 9
So, does the Laurent series of an analytic function f allow convergence outside of the RoC for the normal power series of f?--Rgilhamw 19:50, 25 November 2009 (UTC)
I don't think so. It seems like the laurent series is just another power series representation of the function with another ROC. Like the example in the book 1/(1-z) can be represented by a power series with negative powers of z but with ROC abs(z)>1 instead of less than 1. The Laurent series seems like it is used to represent an analytic function in the annulus $ r<z-c<R $ where c is the center of the annulus.< --Adrian Delancy
