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Yes, of course, after we shrink $U$. A convergent Taylor series at a real point converges in some complex neighborhood of this point. Added reply to your comment: you can apply identity theorem. Two real analytic functions coinciding on an open set of $R^n$ coincide in a complex neighborhood of this set. |
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Yes, of course, after we shrink $U$. A convergent Taylor series at a real point converges in some complex neighborhood of this point. |
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