examples of periodic functions
We list common periodic functions. In the parentheses, there are given their period with least modulus^{}.

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Oneperiodic functions^{} with a real period:
sine ($2\pi $), cosine ($2\pi $), tangent^{} ($\pi $), cotangent ($\pi $), secant ($2\pi $), cosecant ($2\pi $), and functions depending on them – especially the triangularwave function ($2\pi $); the mantissa function $x\lfloor x\rfloor $ (1).

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Oneperiodic functions with an imaginary (http://planetmath.org/ImaginaryNumber) period:
exponential function^{} ($2i\pi $), hyperbolic sine^{} ($2i\pi $), hyperbolic cosine ($2i\pi $), hyperbolic tangent ($i\pi $), hyperbolic cotangent ($i\pi $), and functions depending on them.

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Twoperiodic functions: elliptic functions^{}.

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Functions with infinitely (http://planetmath.org/Infinite^{}) many periods:
the Dirichlet’s function
$f:x\mapsto $ $\{\begin{array}{cc}1\hfill & \text{when}x\in \mathbb{Q}\hfill \\ 0\hfill & \text{when}x\in \mathbb{R}\setminus \mathbb{Q}\hfill \end{array}$ has any rational number as its period; a constant function^{} has any number as its period.
Title  examples of periodic functions 
Canonical name  ExamplesOfPeriodicFunctions 
Date of creation  20130322 17:57:29 
Last modified on  20130322 17:57:29 
Owner  pahio (2872) 
Last modified by  pahio (2872) 
Numerical id  10 
Author  pahio (2872) 
Entry type  Example 
Classification  msc 30A99 
Classification  msc 26A09 
Synonym  common periodic functions 
Related topic  PeriodicityOfExponentialFunction 
Related topic  HyperbolicIdentities 
Related topic  RationalAndIrrational 
Related topic  PeriodicFunctions 
Related topic  FloorFunction 
Related topic  Floor 