3. For each of the following complex functions, (i) determine a power series for the function f(z) centered at the complex number a, and (ii) [ACS] determine the radius of convergence of this power series. (a) f(z) = e³z, a = 0;
3. For each of the following complex functions, (i) determine a power series for the function f(z) centered at the complex number a, and (ii) [ACS] determine the radius of convergence of this power series. (a) f(z) = e³z, a = 0;
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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3a
![3.
For each of the following complex functions, (i) determine a power series for the function f(z)
centered at the complex number a, and (ii) [ACS] determine the radius of convergence of this
power series.
(a) f(2)=e³z, a = 0;
(b) f(z) = 3 sin z - 8 cos z, a = 0;
(c) f(2)= 5-2₂, a = 0;](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F490cbcd2-ad81-426b-824f-903aced284ba%2Fc6eb2178-5857-4b8a-969e-2dbb682d0949%2F571ark_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
For each of the following complex functions, (i) determine a power series for the function f(z)
centered at the complex number a, and (ii) [ACS] determine the radius of convergence of this
power series.
(a) f(2)=e³z, a = 0;
(b) f(z) = 3 sin z - 8 cos z, a = 0;
(c) f(2)= 5-2₂, a = 0;
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