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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
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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(a) A meromorphic function f(z) has the following Laurent series expansion about the point z = i: (-5)k+2(z – i)k Σ f (z) = (k + 5)! k=-5 Define 6f"(z) +7e™z g(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.
Transcribed Image Text:(a) A meromorphic function f(z) has the following Laurent series expansion about the point z = i: (-5)k+2(z – i)k Σ f (z) = (k + 5)! k=-5 Define 6f"(z) +7e™z g(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.
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