Show that the series expansion for arctan(z) = z -z^3/3 + z^5/5 - z^7/7 + .... .

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- May 27th 2009, 02:14 PMkiwijoey(Laurent) Series Expansion
Show that the series expansion for arctan(z) = z -z^3/3 + z^5/5 - z^7/7 + .... .

- May 27th 2009, 02:52 PMKrizalid
start by using $\displaystyle \arctan z=\int_{0}^{z}{\frac{dt}{1+t^{2}}}=\int_{0}^{z}{\l eft( \sum\limits_{j=0}^{\infty }{\left( -t^{2} \right)^{j}} \right)\,dt}.$