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.

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Answered: 26.2. Suppose that f(z) is analytic and…

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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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.