Triangle Wave
المؤلف:
Trott, M
المصدر:
M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004. http://www.mathematicaguidebooks.org/.
الجزء والصفحة:
...
25-5-2019
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Triangle Wave
Analytic representations the symmetric triangle wave with period 2 and varying between 
and 1 include
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
![f(x)=i/(pi^2e^(piix))[Phi(x,2,1/2)-e^(2piix)Phi(-e^(2piix),2,1/2)],](http://mathworld.wolfram.com/images/equations/TriangleWave/NumberedEquation2.gif) |
(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/.
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