Let the function f CC be a doubly periodic function, which means thatfor 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.

Given that f is a doubly periodic function, it satisfies the property: f(z+α)=f(z+β)=f(z) for…

Answered: Let the function f CC be a doubly…

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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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.