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 spaces, which are infinite-dimensional and within which most functions are 'anonymous', with special functions picked out by properties such as symmetry, or relationship to harmonic analysis and group representations.


Elementary functions

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Elementary functions are functions built from basic operations (e.g. addition, exponentials, logarithms...)

Algebraic functions

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Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients.

Elementary transcendental functions

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Transcendental functions are functions that are not algebraic.

Piecewise special functions

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Antiderivatives of elementary functions

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Name Symbol Formula
Logarithmic integral    
Exponential integral    
   
Sine integral    
   
Cosine integral    
   
Error function    
Complementary error function    
Fresnel integrall    
   
Dawson function    
Faddeeva function    
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Name Notation Formula
Gaussian Hypergeometric Function    
Confluent hypergeometric function    
   
Generalized hypergeometric function    
Associated Legendre functions    
   
Meijer G-function    
Fox H-function    
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Other standard special functions

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Miscellaneous functions

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See also

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[[Category:Calculus|Functions] [[Category:Mathematics-related lists|Functions] [[Category:Number theory|Functions] [[Category:Functions and mappings| ]