(a)A meromorphic function f(z) has the following Laurent series expansion about thepoint z = i:(-5)k+2(z – i)kΣf (z) =(k + 5)!k=-5Define6f"(z) +7e™zg(z) =25(z – i)Find the order of the pole about z = i of the function g(z) and calculate Res(g, i),leaving your answer in exact form.

Given that, fz=∑k=-5∞-5k+2z-ikk+5! . . . (1) and gz=6f"z+7eπx25z-i . . . (2) Now ,…

A meromorphic function f(z) has the following Laurent series expansion about the point z = i: (a) 00 (-5)**2(z – i)* f(z) = Σ (k + 5)! k=-5 Define 6f"(z) + 7e™z 25(z – i) g(z) = Find the order of the pole about z = i of the function g(z) and calculate Res(g, i), leaving your answer in exact form.

A meromorphic function f(z) has the following Laurent series expansion about the point z = i: (a) 00 (-5)**2(z – i)* f(z) = Σ (k + 5)! k=-5 Define 6f"(z) + 7e™z 25(z – i) g(z) = Find the order of the pole about z = i of the function g(z) and calculate Res(g, i), leaving your answer in exact form.

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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