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Suppose f has a zero of order k at zo. Show that ‹ƒ′(²). f(z); ²0) = k. Res( (Hint: Express ƒ(z) = (z − zo)³p(z).)

Suppose f has a zero of order k at zo. Show that ‹ƒ′(²). f(z); ²0) = k. Res( (Hint: Express ƒ(z) = (z − zo)³p(z).)

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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Suppose f has a zero of order k at zo. Show that f(z) f(z) Res( (Hint: Express ƒ(z) = (z − zo)ky(z).) -; 20) = k.
Transcribed Image Text:Suppose f has a zero of order k at zo. Show that f(z) f(z) Res( (Hint: Express ƒ(z) = (z − zo)ky(z).) -; 20) = k.
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