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Math Help - Analytic continuation

  1. #1
    Newbie Klaus's Avatar
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    Analytic continuation

    Hello,
    I'm trying to understand analytic continuation:
    Let f and g be two analytic functions.
    If f=g on an open subset of \mathbb{C}, then f=g on any larger connected subset.
    Let f be 1+x+\frac{x^2}{2!} and g be 1+x+\frac{x^2}{2!}+\frac{x^3}{3!} these two analytic functions.


    f=g on the open subset of \mathbb{C} ]-0.1;0.1[, but f\not=g on the larger connected subset \mathbb{R} !

    Where is the problem ?
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  2. #2
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    mr fantastic's Avatar
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    Quote Originally Posted by Klaus View Post
    Hello,
    I'm trying to understand analytic continuation:
    Let f be 1+x+\frac{x^2}{2!} and g be 1+x+\frac{x^2}{2!}+\frac{x^3}{3!} these two analytic functions.


    f=g on the open subset of \mathbb{C} ]-0.1;0.1[, but f\not=g on the larger connected subset \mathbb{R} !

    Where is the problem ?
    There's no problem. f \neq g on (-0.1, 0.1). In fact, they are only equal at x = 0 .....
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