List of mathematical functions: Difference between revisions

Revision as of 16:07, 11 March 2022

Revision as of 14:12, 5 April 2022

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** [[Common logarithm]]

** [[Binary logarithm]]

* [[Exponentiation#Power_functionsPower functions|Power functions]]: raise a variable number to a fixed power; also known as [[Allometric function]]s; note: if the power is a rational number it is not strictly a transcendental function.

* [[Periodic function]]s

** [[Trigonometric function]]s: [[sine]], [[cosine]], [[tangent (trigonometry)|tangent]], [[cotangent]], [[secant (trigonometry)|secant]], [[cosecant]], [[exsecant]], [[excosecant]], [[versine]], [[coversine]], [[vercosine]], [[covercosine]], [[haversine]], [[hacoversine]], [[havercosine]], [[hacovercosine]], etc.; used in [[geometry]] and to describe periodic phenomena. See also [[Gudermannian function]].

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* [[Absolute value]]: distance to the origin (zero point)

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===[[Arithmetic_function|Arithmetic functionsfunction]]s===

* [[divisor function|Sigma function]]: [[Summation|Sums]] of [[Exponentiation|power]]s of [[divisor]]s of a given [[natural number]].

* [[Euler's totient function]]: Number of numbers [[coprime]] to (and not bigger than) a given one.

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* [[Partition function (number theory)|Partition function]]: Order-independent count of ways to write a given positive integer as a sum of positive integers.

* [[Möbius function|Möbius μ function]]: Sum of the nth primitive roots of unity, it depends on the prime factorization of n.

* [[Prime omega function|Prime omega functions]]s

* [[Chebyshev function|Chebyshev functions]]s

* [[Liouville function]], λ(''n'') = (–1)^Ω(''n'')

* [[Von Mangoldt function]], Λ(''n'') = log ''p'' if ''n'' is a positive power of the prime ''p''

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** [[Dedekind eta function]]

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===Bessel and related functions===

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* [[Synchrotron function]]

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===Riemann zeta and related functions===

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* [[Riesz function]]

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===Hypergeometric and related functions===

* [[Hypergeometric function]]s: Versatile family of [[power series]].

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* [[Super-root]]s

* [[Tetration]]

===Other standard special functions===

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* [http://eqworld.ipmnet.ru/en/auxiliary/aux-specfunc.htm Special functions] at EqWorld: The World of Mathematical Equations.

[[Category:Calculus|Functions]]

[[Category:Mathematics-related lists|Functions]]

[[Category:Number theory|Functions]]

[[Category:Functions and mappings| ]]

[[pl:Funkcje elementarne]]