Question: Assume that |z| <1.Iftan-1(z)be the principal branch of the inversetangent (tan-1(0)=0), then show that tan-1(z)=0zdw1+w2. Use thegeometric series 11+w2=n=0(-1)nw2n and the integral representationabove to find

Assume that |z|<1.Iftan-1(z)be the principal branch of the inversetangent (tan-1(0)=0), then show that tan-1(z)=0zdw1+w2. Use thegeometric series 11+w2=n=0(-1)nw2n and the integral representationabove to find the Taylor series for tan-1(z) about z=0.

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