Convergence of Taylor series in several variables

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where do a multiple Taylor series converge ??

i mean if given a function [tex] f(x,y) [/tex] can i expand this f into a double Taylor series that will converge on a rectangle ? for example , if one can ensure that it converges for |x| <1 and |y| <1
 

mathman

Science Advisor
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It depends very much on what f is.
 

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