Suppose that f, g € H(D(z, r)), 1 < m < n, f has a zero of order z and g has a zero of order m at z. Show that f/g has a removable larity at z.
Suppose that f, g € H(D(z, r)), 1 < m < n, f has a zero of order z and g has a zero of order m at z. Show that f/g has a removable larity at z.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 54EQ
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Step 1
An isolated singularity of the function is called removable if the function can be defined at so that it become analytic at .
From the question f and g are analytic on an open set D and f has a zero of order n and g has a zero of order m at z .
let the function f and g are defined as:
Step 2
Now the function is defined as:
Step 3
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