Show that if P(z) is a polynomial of degree n then f(z) = is holomorphic on C \ P(z) {z1,..., zm}, where 1 < m < n. Show that each zk is a pole singularity for f, and if nk is the order of the pole zp then nk = n.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1
is holomorphic on C \
P(2)
Show that if P(z) is a polynomial of degree n then f(z)
{z1, ..., zm}, where 1 < m < n. Show that each zk is a pole singularity for f, and if nk is
the order of the pole zk then E=1nk = n.
Transcribed Image Text:1 is holomorphic on C \ P(2) Show that if P(z) is a polynomial of degree n then f(z) {z1, ..., zm}, where 1 < m < n. Show that each zk is a pole singularity for f, and if nk is the order of the pole zk then E=1nk = n.
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