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2.1 Consider the power series n(2 - 2+3i)2". (a) If 0< L

2.1 Consider the power series n(2 - 2+3i)2". (a) If 0< L

Advanced Engineering Mathematics
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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2.1 Consider the power series a„(z – 2+ 3i)2". (a) If 0 < L< oo is the radius of convergence of the given series, what is lim 1n+? an (Possibly in terms of L). (b) If the radius of convergence of the above series is L = 0, what conclusion can be made about the convergence of the given series? 2.2 Prove that e -dz z2 + 7+1 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3. 2.3 Evaluate the integral 7 3i sinh? (z – 2i)4 dz, z + 4 - 2i where C is the circle |z – 2i|| results you used to arrive at your final answer. = 4 traversed once anticlockwise. State clearly which
Transcribed Image Text:2.1 Consider the power series a„(z – 2+ 3i)2". (a) If 0 < L< oo is the radius of convergence of the given series, what is lim 1n+? an (Possibly in terms of L). (b) If the radius of convergence of the above series is L = 0, what conclusion can be made about the convergence of the given series? 2.2 Prove that e -dz z2 + 7+1 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3. 2.3 Evaluate the integral 7 3i sinh? (z – 2i)4 dz, z + 4 - 2i where C is the circle |z – 2i|| results you used to arrive at your final answer. = 4 traversed once anticlockwise. State clearly which
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