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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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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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.
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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