) Evaluate the following integrals:i) .

Question

) Evaluate the following integrals:
i) $I = \int_{0}^{2\pi} f(e^{i\theta}) \cos^2(\theta/2) \, d\theta$ .

ii) $I = \int_{0}^{2\pi} f(e^{i\theta}) \sin^2 \theta/2 \, d\theta$ .

09 Jan 2026

Answer :

Word Count : 95

Let (f) be analytic on and inside the unit circle and write its Taylor expansion [ f(z)=a_0+a_1 z+a_2 z^2+\cdots , \qquad z=e^{i\theta}. ] ______ ________ ___ _____ ______ ___ ____ _______ _________ ______.
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