Periodic Functions

Ravi P. Agarwal (), Kanishka Perera () and Sandra Pinelas ()
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Ravi P. Agarwal: Florida Institute of Technology, Department of Mathematics
Kanishka Perera: Florida Institute of Technology, Department of Mathematical Sciences
Sandra Pinelas: Azores University, Department of Mathematics

Chapter Lecture 45 in An Introduction to Complex Analysis, 2011, pp 298-302 from Springer

Abstract: Abstract Recall from Lecture 8 that a complex number ω ≠ 0 is a period of a function f(z) if f(z + ω) = f(z) for all z. For example,e z has the period 2πi, and sin z and cos z have the period 2π. If ω1 and ω2 are periods of f(z), then $$f(z + \omega _1 + \omega _2 )\, = \,f(z + \omega _1 ){\rm } = {\rm }f(z);$$ i.e., ω 1+ω 2 is also a period. In particular, if ω is a period, then nω is also a period, where n is any integer.

Date: 2011
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DOI: 10.1007/978-1-4614-0195-7_45

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