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20.7. Show that the following functions are entire: e2z (a) f(z) = 2 e"-1-? for z # 0, sin z for z + 0, (b) f(z) = 1 for z = 0. for z = 0. COS Z z # ±n/2, for 22 – n² /4 -1/T (c) f(2) = for z = 士不/2.

20.7. Show that the following functions are entire: e2z (a) f(z) = 2 e"-1-? for z # 0, sin z for z + 0, (b) f(z) = 1 for z = 0. for z = 0. COS Z z # ±n/2, for 22 – n² /4 -1/T (c) f(2) = for z = 士不/2.

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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The question is about complex series.

( z ) is a complex number.

Please solve parts a, b and c.

20.7. Show that the following functions are entire: e1- for z +0, sin z for z + 0, (a) f(z) = (b) f(2) = for z = = 0. for z = 0. COS Z A for z # ±m/2, (c) f(z) = -1/T for z = ±7/2.
Transcribed Image Text:20.7. Show that the following functions are entire: e1- for z +0, sin z for z + 0, (a) f(z) = (b) f(2) = for z = = 0. for z = 0. COS Z A for z # ±m/2, (c) f(z) = -1/T for z = ±7/2.
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