Convergence of Taylor series in several variables

[zetafunction]

where do a multiple Taylor series converge ??

i mean if given a function $$f(x,y)$$ 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]

It depends very much on what f is.