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I was looking for the exact formulation of taylor's theorem for a complex-valued function of a real argument, i.e., for $f:\mathbb{R}\rightarrow\mathbb{C}$? Can anyone provide such a formulation or a reference where to find it? many thanks, any help is much appreciated!

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The formulation does not differ from the regular Taylor's theorem. If you have a complex-valued polynomial $p(x)$ where $x$ is a real variable, then you can write $p(x) = g(x) + i h(x)$, where $g,h$ are real-valued polynomials, and you can apply Taylor's theorem to each of $g,h$ and recombine. – Christopher A. Wong Oct 23 '12 at 2:48

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