List of mathematical functions: Difference between revisions

Revision as of 14:01, 18 May 2020

Revision as of 06:25, 21 May 2020

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==[[Special functions]]==

===Basic special functions===

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* [[Indicator function]]: maps ''x'' to either 1 or 0, depending on whether or not ''x'' belongs to some subset.

* [[Step function]]: A finite [[linear combination]] of [[indicator function]]s of [[half-open interval]]s.

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* [[Sign function]]: Returns only the sign of a number, as +1 or −1.

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

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===[[Arithmetic_function|Number theoretic functions]]===

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

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===Elliptic and related functions===

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* [[Elliptic integral]]s: Arising from the path length of [[ellipse]]s; important in many applications. Related functions are the [[quarter period]] and the [[nome (mathematics)|nome]]. Alternate notations include:

** [[Carlson symmetric form]]

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** [[J-invariant]]

** [[Dedekind eta function]]

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===Bessel and related functions===

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* [[Airy function]]

* [[Bessel function]]s: Defined by a [[differential equation]]; useful in [[astronomy]], [[electromagnetism]], and [[mechanics]].

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* [[Laguerre polynomials]]

* [[Chebyshev polynomials]]

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===Riemann zeta and related functions===

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* [[Riemann zeta function]]: A special case of [[Dirichlet series]].

* [[Riemann Xi function]]

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** [[Spence's function]]

* [[Riesz function]]

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===Hypergeometric and related functions===

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

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===Iterated exponential and related functions===

* [[Hyper operator]]s

* [[Iterated logarithm]]

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* [[Tetration]]

* [[Lambert W function]]: Inverse of ''f''(''w'') = ''w'' exp(''w'').

===Other standard special functions===

* Dirichlet lambda function, ''λ''(''s'') = (1 – 2^−''s'')ζ(''s'') where ''ζ'' is the [[Riemann zeta function]]

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

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* [[Synchrotron function]]

* [[Arithmetic–geometric mean]]

===Miscellaneous functions===

===Miscellaneous functions===

* [[Ackermann function]]: in the [[theory of computation]], a [[computable function]] that is not [[primitive recursive function|primitive recursive]].

* [[Böttcher's equation|Böttcher's function]]

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* [[Minkowski's question mark function]]: Derivatives vanish on the rationals.

* [[Weierstrass function]]: is an example of [[continuous function]] that is nowhere [[Differentiable function|differentiable]]

== See also ==

*[[List of mathematical abbreviations]]