26.1. Locate and determine the order of zeros of the following functions: (a). e2z - e, (b). z2 sinh z, (c). zcos? z, (d). z cos z. 26.2. Suppose that f(z) is analytic and has a zero of order m at zo- Show that (a). f'(z) has a zero of order m-1 at zo. (b). f'(z)/f(z) has a simple pole at zo.
26.1. Locate and determine the order of zeros of the following functions: (a). e2z - e, (b). z2 sinh z, (c). zcos? z, (d). z cos z. 26.2. Suppose that f(z) is analytic and has a zero of order m at zo- Show that (a). f'(z) has a zero of order m-1 at zo. (b). f'(z)/f(z) has a simple pole at zo.
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:26.1. Locate and determine the order of zeros of the following functions:
(a). e2 - e, (b). z2 sinh z, (c). z4cos? z, (d). z cos z.
26.2. Suppose that f(2) is analytic and has a zero of order m at zo-
Show that
(a). f'(z) has a zero of order m
1 at zo-
(b). f'(z)/f(z) has a simple pole at zo.
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