3. Write down a function f which is analytic in C except for z = 0,1, 2, and which has an essential singularity at z = 0, a removable singularity at z = 1, and a pole of order 5 at z = 2, with residue 14. There are many correct solutions: think about writing f as a sum of three functions, each of which has a single isolated singularity.
3. Write down a function f which is analytic in C except for z = 0,1, 2, and which has an essential singularity at z = 0, a removable singularity at z = 1, and a pole of order 5 at z = 2, with residue 14. There are many correct solutions: think about writing f as a sum of three functions, each of which has a single isolated singularity.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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I've attached the question, along with my attempt at a solution. Is my example right? The first term is what I chose for a removable singularity at 1, the second term for a pole of order 5, and the last as an essential singularity at 0. The part I'm not completely sure about is if the residue of the function is 14. I know that removable singularities have a residue of 0, and that the essential singularity has a residue of 1. Then I figured I needed to get a function with a residue of 13 in order to have a total residue of 14. Can you verify/correct my work? Or provide a different solution? Thank you.
Transcribed Image Text:3. Write down a function f which is analytic in C except for z = 0, 1, 2, and which has an
essential singularity at z = 0, a removable singularity at z = 1, and a pole of order 5 at
z = 2, with residue 14. There are many correct solutions: think about writing f as a sum
of three functions, each of which has a single isolated singularity.
Let f(2) =
13z4
(z-2)5 +e/z
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