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(a) Find the coefficients an and b₁ of the Laurent series Žª Σan (z −zo)" + [bn(z-zo)¯n n=0 n=1 of the function f(z) = (z-1)(z+8) about zo = 1. Justify all of your steps. (b) Determine the residue of the function f(z) from part (a) at the point z = -8. State all the propositions (theorems) that you are using and justify all of your steps.

(a) Find the coefficients an and b₁ of the Laurent series Žª Σan (z −zo)" + [bn(z-zo)¯n n=0 n=1 of the function f(z) = (z-1)(z+8) about zo = 1. Justify all of your steps. (b) Determine the residue of the function f(z) from part (a) at the point z = -8. State all the propositions (theorems) that you are using and justify all of your steps.

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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Question 4 (a) Find the coefficients an and bn of the Laurent series Σan(z − zo)” + [bn(z – zo)¯n n=0 n=1 of the function f(z) = (z-1){(z+8) about zo = 1. Justify all of your steps. (b) Determine the residue of the function f(z) from part (a) at the point z = -8. State all the propositions (theorems) that you are using and justify all of your steps.
Transcribed Image Text:Question 4 (a) Find the coefficients an and bn of the Laurent series Σan(z − zo)” + [bn(z – zo)¯n n=0 n=1 of the function f(z) = (z-1){(z+8) about zo = 1. Justify all of your steps. (b) Determine the residue of the function f(z) from part (a) at the point z = -8. State all the propositions (theorems) that you are using and justify all of your steps.
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