Triangle Wave

Analytic representations the symmetric triangle wave with period 2 and varying between  and 1 include

			(1)
			(2)
			(3)

where  is the fractional part of .

The triangle wave is implemented in the Wolfram Language as TriangleWave[x].

The Fourier series for the triangle wave is given by

(4)

which can be summed to yield the analytic expression

(5)

where  is a Lerch transcendent.

A form of triangle wave ranging between 0 and 1 with period 2 is given by

(6)

(Trott 2004, p. 228), where  is the nearest integer function.

REFERENCES:

Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004. http://www.mathematicaguidebooks.org/.