Question
Evaluate the following integrals:
i) .
ii)
Answer :
Word Count : 124
Assume that (f(z)) is analytic on and inside the unit circle and has the power series expansion (f(z)=\sum_{n=0}^{\infty} a_n z^n). Then (f(e^{i\theta})=\sum_{n=0}^{\infty} a_n e^{in\theta}). Using [ \cos^2\frac{\theta}{2}=\frac{1+\cos\theta}{2}, \qquad \sin^2\frac{\theta}{2}=\frac{1-\cos\theta}{2}, ] we _____ ________ ________ _________ ____ __________ _________ _____ _________ ________ __________ ____.
_______ __________ _______ _______ ___ __________ __________ ________.
________ ______ _________ ___ ________ ______ ___ _______ ____.
_______ ______ _____ __________ __________ ____ _______ ______ _________ ___ __________.
_______ __________ _____ ____ ________ _____ __________ _________ _____ _______ _____.
_____ ____ _______ ___ ______ ___ __________ __________ ________ _____ ______ __________.
________ ____ ______ _________ _____ ______ ____ _________.
_____ ___ _________ _____ _______ _________ ______ ________.
______ ______ ___ ______ __________ _____ _________ _______ _______ ____.
_________ ____ ______ __________.
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Assume that (f(z)) is analytic on and inside the unit circle and has the power series expansion (f(z)=\sum_{n=0}^{\infty} a_n z^n). Then (f(e^{i\theta})=\sum_{n=0}^{\infty} a_n e^{in\theta}). Using [ \cos^2\frac{\theta}{2}=\frac{1+\cos\theta}{2}, \qquad \sin^2\frac{\theta}{2}=\frac{1-\cos\theta}{2}, ] we _____ ________ ________ _________ ____ __________ _________ _____ _________ ________ __________ ____.
_______ __________ _______ _______ ___ __________ __________ ________.
________ ______ _________ ___ ________ ______ ___ _______ ____.
_______ ______ _____ __________ __________ ____ _______ ______ _________ ___ __________.
_______ __________ _____ ____ ________ _____ __________ _________ _____ _______ _____.
_____ ____ _______ ___ ______ ___ __________ __________ ________ _____ ______ __________.
________ ____ ______ _________ _____ ______ ____ _________.
_____ ___ _________ _____ _______ _________ ______ ________.
______ ______ ___ ______ __________ _____ _________ _______ _______ ____.
_________ ____ ______ __________.
Get Full Answer on WhatsApp
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