(a) Let z be any complex number, and let C denote the unit circle

in the w plane. Then use that contour in expression (5), Sec. 60, for the coefficients in a Laurent series, adapted to such series about the origin in the w plane, to show that

Where

(b) With the aid of Exercise 5, Sec. 38, regarding certain definite integrals of even and odd complex-valued functions of a real variable, show that the coefficients in part (a) here can be written€ 

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