Consider the function Where q is analytic at z0, q(z0) = 0, and q'(z0) 0. Show that

Question:

Consider the function

Where q is analytic at z0, q(z0) = 0, and q'(z0) ‰ 0. Show that z0 is a pole of order m = 2 of the function f, with residue

Suggestion: that z0 is a zero of order m = 1 of the function
q, so that
q(z) = (z ˆ’ z0)g(z)
Where g(z) is analytic and nonzero at z0. Then write

The desired form of the residue B0 = Ï†' (z0) can be obtained by showing that
q'(z0) = (z0) and q'' (z0) = 2g' (z0).

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Complex Variables and Applications

ISBN: 978-0073051949

8th edition

Authors: James Brown, Ruel Churchill

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Question Posted: Jun 01, 2016 01:44 AM

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Consider the function Where q is analytic at z0, q(z0) = 0, and q'(z0) 0. Show that

Question:

f(z) [a(2)12 q" (z0) ф(z) f(z)--ф(2) g(2)] 2

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We are given that fz 1 qz 2 where q is analytic at ...View the full answer

Complex Variables and Applications

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