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单词 ExamplesOfPeriodicFunctions
释义

examples of periodic functions


We list common periodic functions. In the parentheses, there are given their period with least modulusMathworldPlanetmathPlanetmathPlanetmath.

  • One-periodic functionsMathworldPlanetmath with a real period:

    sine (2π), cosine (2π), tangentMathworldPlanetmathPlanetmathPlanetmath (π), cotangent (π), secant (2π), cosecant (2π), and functions depending on them – especially the triangular-wave function (2π);  the mantissa functionx-x (1).

  • One-periodic functions with an imaginary (http://planetmath.org/ImaginaryNumber) period:

    exponential functionDlmfDlmfMathworldPlanetmath (2iπ), hyperbolic sineMathworldPlanetmath (2iπ), hyperbolic cosine (2iπ), hyperbolic tangent (iπ), hyperbolic cotangent (iπ), and functions depending on them.

  • Two-periodic functions:  elliptic functionsMathworldPlanetmath.

  • Functions with infinitely (http://planetmath.org/InfiniteMathworldPlanetmath) many periods:

    the Dirichlet’s function

    f:x{1whenx0whenx

    has any rational number as its period;  a constant functionMathworldPlanetmath has any number as its period.

Titleexamples of periodic functions
Canonical nameExamplesOfPeriodicFunctions
Date of creation2013-03-22 17:57:29
Last modified on2013-03-22 17:57:29
Ownerpahio (2872)
Last modified bypahio (2872)
Numerical id10
Authorpahio (2872)
Entry typeExample
Classificationmsc 30A99
Classificationmsc 26A09
Synonymcommon periodic functions
Related topicPeriodicityOfExponentialFunction
Related topicHyperbolicIdentities
Related topicRationalAndIrrational
Related topicPeriodicFunctions
Related topicFloorFunction
Related topicFloor
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