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Date: 3-9-2019
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Date: 18-8-2018
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Date: 25-3-2019
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Analytic representations the symmetric triangle wave with period 2 and varying between and 1 include
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(1) |
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(2) |
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(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
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(4) |
which can be summed to yield the analytic expression
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(5) |
where is a Lerch transcendent.
A form of triangle wave ranging between 0 and 1 with period 2 is given by
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(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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دراسة: عدم ترتيب الغرفة قد يدل على مشاكل نفسية
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علماء: تغير المناخ تسبب في ارتفاع الحرارة خلال موسم الحج
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جهود مكثفة وطباعة عشرات الآلاف من المنشورات .. استعدادات العتبة العلوية المقدسة لعيد الغدير الأغر
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