For z + 5i, let g(2) = (z – 5i)Log(z – 5i) + (z – 5i) where Log is the principal logarithm. Find a power series (i.e., Taylor series) for g(z) centered at z0 = 0 (not 5i) and specify the coefficients cg for k E NU {0}. What is the largest possible radius of convergence? DRAW STUFF and be sure to show your steps.
For z + 5i, let g(2) = (z – 5i)Log(z – 5i) + (z – 5i) where Log is the principal logarithm. Find a power series (i.e., Taylor series) for g(z) centered at z0 = 0 (not 5i) and specify the coefficients cg for k E NU {0}. What is the largest possible radius of convergence? DRAW STUFF and be sure to show your steps.
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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Transcribed Image Text:For z + 5i, let
9(2) = (z – 5i)Log(2 – 5i) + (z – 5i)
where Log is the principal logarithm. Find a power series (i.e., Taylor series) for g(z) centered at
zo = 0 (not 5i) and specify the coefficients C for k E NU {0}. What is the largest possible radius
of convergence? DRAW STUFF and be sure to show your steps.
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