My Math Forum Even and odd periodic extensions

 Applied Math Applied Math Forum

 November 9th, 2016, 11:27 AM #1 Newbie   Joined: Nov 2016 From: South Africa Posts: 2 Thanks: 0 Even and odd periodic extensions Consider the piecewise function, $f(x)=\left\{\begin{array}{r|r}x+4 & 0 < x < 2\\0 & 2 < x < 3\\\end{array}\right\}$ ---------- The odd periodic extension $F^O (x)$ of $f(x)$ is defined as: $F^O (x)=\left\{\begin{array}{r|r}0 & -3 < x < -2\\x-4 & -2 < x < 0\\x+4 & 0 < x < 2\\0 & 2 < x < 3\\\end{array}\right\}$ where $F^O (x)$ has a period of 6. ---------- The odd periodic extension $F^O (x)$ of $f(x)$ is defined as: $F^e (x)=\left\{\begin{array}{r|r}0 & -3 < x < -2\\-x+4 & -2 < x < 0\\x+4 & 0 < x < 2\\0 & 2 < x < 3\\\end{array}\right\}$ where $F^e (x)$ has a period of 6. ---------- Does the notation used expressions $F^O (x)$ and $F^e (x)$ represent periodic extensions of $f (x)$ that repeats indefinitely every six units? What other notation can be used to present a periodic function of a piecewise function?
 November 9th, 2016, 01:49 PM #2 Global Moderator   Joined: May 2007 Posts: 6,306 Thanks: 525 By definition a periodic expression of period 6 repeats every 6 units. The notation you use is as good as any.

 Tags extensions, odd, periodic

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Epsilon90 Abstract Algebra 4 November 28th, 2013 01:49 AM declan Abstract Algebra 5 May 7th, 2010 07:54 AM shakeydakey Abstract Algebra 1 October 27th, 2009 11:15 AM conradtsmith Calculus 1 August 20th, 2009 04:36 AM TTB3 Abstract Algebra 0 April 2nd, 2009 10:41 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top