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Owen Reich (talk | contribs) m Added the rad function (as in the ABC Conjecture), and added a definition for the Carmichael function. |
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{{Short description|none}}
In [[mathematics]], some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of [[special functions]] which developed out of [[statistics]] and [[mathematical physics]]. A modern, abstract point of view contrasts large [[function space]]s, which are infinite-dimensional and within which most functions are
See also [[List of types of functions]]
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===Algebraic functions===
[[Algebraic function]]s are functions that can be expressed as the solution of a polynomial equation with
* [[Polynomial]]s: Can be generated solely by addition, multiplication, and raising to the power of a positive integer.
** [[Constant function]]: polynomial of degree zero, graph is a horizontal straight line
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* [[Prime omega function]]s
* [[Chebyshev function]]s
* [[Liouville function]]
* [[Von Mangoldt function]], Λ(''n'') = log ''p'' if ''n'' is a positive power of the prime ''p''
* [[Carmichael function]]: <math>\lambda(n)=</math> The smallest integer <math>m</math> such that <math>a^m\equiv 1\pmod{n}</math> for all <math>a</math> coprime to <math>n</math>
* [[Radical of an integer|Radical function]]: The product of the distinct prime factors of a positive integer input.
===Antiderivatives of elementary functions===
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