(4) (a) Find the contour integralde using the Cauchy integral formula, whereC is the positively oriented circle given by |z-il = 2.(b) Let C' be the positively oriented circle given by |z| = 3. If g(z) is a function suchthat g(z) = [22-1-2ds for every 2 € C with [2] # 3, then find g(1) using theCauchy integral formula.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(z-(a+1))" Let f(z) = L n(ß+2)" (n+2)² n(B+2)" (n+2)² · n=1 i) ii) iii Find the region where the function f(z) is analytic. Find f(4) (a+ 1). If C is the positively oriented circle |2 – (a + 1)| = 1. Evaluate f(z) dz. I (z-(a+1))³
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(4) (a) Find the contour integral de using the Cauchy integral formula, where C is the positively oriented circle given by |z-il = 2. (h) Let G be the pe tat