• Source: List of periodic functions

This is a list of some well-known periodic functions. The constant function f (x) = c, where c is independent of x, is periodic with any period, but lacks a fundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.




Smooth functions


All trigonometric functions listed have period



2
π


{\displaystyle 2\pi }

, unless otherwise stated. For the following trigonometric functions:

Un is the nth up/down number,
Bn is the nth Bernoulli number
in Jacobi elliptic functions,



q
=

e

−
π



K
(
1
−
m
)


K
(
m
)







{\displaystyle q=e^{-\pi {\frac {K(1-m)}{K(m)}}}}





Non-smooth functions


The following functions have period



p


{\displaystyle p}

and take



x


{\displaystyle x}

as their argument. The symbol



⌊
n
⌋


{\displaystyle \lfloor n\rfloor }

is the floor function of



n


{\displaystyle n}

and



sgn


{\displaystyle \operatorname {sgn} }

is the sign function.

K means Elliptic integral K(m)




Vector-valued functions


Epitrochoid
Epicycloid (special case of the epitrochoid)
Limaçon (special case of the epitrochoid)
Hypotrochoid
Hypocycloid (special case of the hypotrochoid)
Spirograph (special case of the hypotrochoid)




Doubly periodic functions


Jacobi's elliptic functions
Weierstrass's elliptic function




Notes

Kata Kunci Pencarian:

• Tabel periodik
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• Tren periodik
• Panjang gelombang
• Vladimir Arnold
• Belerang
• Raksa
• Boron
• Selenium
• Terence Tao
• List of periodic functions
• Periodic function
• Trigonometric functions
• List of mathematical functions
• Periodic table
• Triangle wave
• Sine and cosine
• Square wave
• Epicycloid
• Epitrochoid