1. Find the radius of convergence of: k (a) (−1)k (¹+2i) * (z +2i)*. k=0 k (b) Ỹ (−1)² (z − 1 − i)*. - k2k (e) Σ (3+(-1)*)* (²) *. k=0
1. Find the radius of convergence of: k (a) (−1)k (¹+2i) * (z +2i)*. k=0 k (b) Ỹ (−1)² (z − 1 − i)*. - k2k (e) Σ (3+(-1)*)* (²) *. k=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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![1. Find the radius of convergence of:
k
1+2i
(a) Σ(-1)* (¹ + ²i) * (z +2i)*.
2
k=0
(b)
(-1) k
k2k (z − 1 - i)k.
k=1
(©) Σ (³ + (−1)*) * (²) *.
k=0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd377aab-d46d-41ac-a49d-b3119dc6fdc9%2F6e38c670-ae00-44f6-8d45-9716ff23b8b7%2Fohfzkts_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Find the radius of convergence of:
k
1+2i
(a) Σ(-1)* (¹ + ²i) * (z +2i)*.
2
k=0
(b)
(-1) k
k2k (z − 1 - i)k.
k=1
(©) Σ (³ + (−1)*) * (²) *.
k=0
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