1 2z 3 1. Consider the function f(z) (a) Find the power series expansion of f(z) about the point % = O and determine the radius of convergence. Hint: R - 22. (b) Find the power series expansion of f(z) about the point zo = 2 and determine the radius of convergence. Hint: R = 12. (c) Find the power series expansion of f(z) about the point zo determine the radius of convergence. Hint: R = 1. 3 = 2/+i and (d) Draw the various discs of convergence in each of (a) - (c) and discuss your answers in the context of the results we have stated on power/Taylor series.
1 2z 3 1. Consider the function f(z) (a) Find the power series expansion of f(z) about the point % = O and determine the radius of convergence. Hint: R - 22. (b) Find the power series expansion of f(z) about the point zo = 2 and determine the radius of convergence. Hint: R = 12. (c) Find the power series expansion of f(z) about the point zo determine the radius of convergence. Hint: R = 1. 3 = 2/+i and (d) Draw the various discs of convergence in each of (a) - (c) and discuss your answers in the context of the results we have stated on power/Taylor series.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
Related questions
Question
![1
2z 3
1. Consider the function f(z)
(a) Find the power series expansion of f(z) about the point % = O and determine
the radius of convergence. Hint: R
-
22.
(b) Find the power series expansion of f(z) about the point zo = 2 and determine
the radius of convergence. Hint: R = 12.
(c) Find the power series expansion of f(z) about the point zo
determine the radius of convergence. Hint: R = 1.
3
= 2/+i and
(d) Draw the various discs of convergence in each of (a) - (c) and discuss your
answers in the context of the results we have stated on power/Taylor series.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3688a312-1b6e-40d4-973f-537807921925%2F609d08bd-9659-46ab-af4e-1973440898d9%2F0h3nuju_processed.png&w=3840&q=75)
Transcribed Image Text:1
2z 3
1. Consider the function f(z)
(a) Find the power series expansion of f(z) about the point % = O and determine
the radius of convergence. Hint: R
-
22.
(b) Find the power series expansion of f(z) about the point zo = 2 and determine
the radius of convergence. Hint: R = 12.
(c) Find the power series expansion of f(z) about the point zo
determine the radius of convergence. Hint: R = 1.
3
= 2/+i and
(d) Draw the various discs of convergence in each of (a) - (c) and discuss your
answers in the context of the results we have stated on power/Taylor series.
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