Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Odd/even functions and periodicity

  1. Aug 17, 2014 #1
    You can prove if f(x) is an odd function and f(x+ t) is an even function then f(x) is periodic with period at most 4t. Are there other theorems like that?i know this is a somewhat open ended and general question, it's just i would like to squeeze some more results from this angle and can not.
     
  2. jcsd
  3. Aug 17, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    ... what "more results"? "more" suggests you have already got some results. What results have you got so far?

    Consider the specific example where f(x)=sin(x).
    The general approach would start with the definitions of both.

    (modify slightly so that f(x-t) is even, makes it easier to write...)

    if f(-x)=-f(x) and f(t-x)=f(x-t) then f(x)=f(x-nt): n in Z (?)

    for f(x)=sin(x), t=pi/2, n=4.
     
  4. Aug 17, 2014 #3
    The result so far is that if f(x) is odd and f(x+t) is even then f(n2t) =0 for all integer n, f(x) is periodic, and the minimum period is no greater than 4t.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Odd/even functions and periodicity
  1. Even or Odd Functions? (Replies: 6)

Loading...