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Let the function f CC be a doubly periodic function, which means that for non-zero complex numbers a, ß, with a/ẞ & R, f(z+a) = f(z+Bẞ) = f(z) for all z = C. Prove that every entire function that is doubly periodic is constant.

Let the function f CC be a doubly periodic function, which means that for non-zero complex numbers a, ß, with a/ẞ & R, f(z+a) = f(z+Bẞ) = f(z) for all z = C. Prove that every entire function that is doubly periodic is constant.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 35E
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Let the function f CC be a doubly periodic function, which means that for non-zero complex numbers a, ß, with a/ẞ & R, f(z+a) = f(z+ B) = f(z) for all z = C. Prove that every entire function that is doubly periodic is constant.
Transcribed Image Text:Let the function f CC be a doubly periodic function, which means that for non-zero complex numbers a, ß, with a/ẞ & R, f(z+a) = f(z+ B) = f(z) for all z = C. Prove that every entire function that is doubly periodic is constant.
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