I need to find the first three terms of this series.(adsbygoogle = window.adsbygoogle || []).push({});

Am I correct in saying z^i = exp(i*Log(z)), then using the taylor series for e^z, giving me:

(i*Log(z)) - 1/2*(Log(z))^2 - i/6*(Log(z))^3 + 1/24*(Log(z))^4 + ....

I haven't worked it out, but this seems to mean that the coefficients for every term in the Taylor series for z^i is actually an infinite series, found by combining terms in the Log(z) Taylor series.

This seems like I could be way off though, so I don't want to do the calculations if I don't have to.

Thanks in advance.

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# Taylor series of z^i at z=i

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