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Given n > 1, define f(z) = 1/z" for z +0. Show that f(z) = U(r, 0) + iV(r, 0) for cos(no) sin(no) U(r, 0) = V (r, 0) : sn pn Deduce that f(2) is holomorphic on the open set A = C \ {0} with f'(2) = Vz E A. zn+1

Given n > 1, define f(z) = 1/z" for z +0. Show that f(z) = U(r, 0) + iV(r, 0) for cos(no) sin(no) U(r, 0) = V (r, 0) : sn pn Deduce that f(2) is holomorphic on the open set A = C \ {0} with f'(2) = Vz E A. zn+1

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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Given n > 1, define f(z) = 1/z" for z + 0. Show that f(z) = U(r,0) + iV(r,0) for U(r, 0) = cos(no) V (r, 0) sin(no) - pn pn Deduce that f(z) is holomorphic on the open set A= C \ {0} with n f'(z) = Vz E A. zn+1
Transcribed Image Text:Given n > 1, define f(z) = 1/z" for z + 0. Show that f(z) = U(r,0) + iV(r,0) for U(r, 0) = cos(no) V (r, 0) sin(no) - pn pn Deduce that f(z) is holomorphic on the open set A= C \ {0} with n f'(z) = Vz E A. zn+1
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