Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical...

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...

This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differential...

A special function register (SFR) is a register within a microcontroller that controls or monitors various aspects of the microcontroller's function. Depending...

In the C++ programming language, special member functions are functions which the compiler will automatically generate if they are used, but not declared...

to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α {\displaystyle \alpha...

Friedrich Gauss had already studied special Jacobi elliptic functions in 1797, the lemniscate elliptic functions in particular, but his work was published...

mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for...

trigonometric functions (occasionally also called antitrigonometric, cyclometric, or arcus functions) are the inverse functions of the trigonometric functions, under...

wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons...

W {\displaystyle W} ⁠ function from a result of Rosenlicht and of Liouville" (PDF). Integral Transforms and Special Functions. 19 (10): 709–712. doi:10...

In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces...

In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula...

In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems...

distinguishing it from some other functions that are also commonly called exponential functions. These functions include the functions of the form ⁠ f ( x ) = b...

Rules for computing derivatives of functions Incomplete gamma function – Types of special mathematical functions Indefinite sum – the inverse of a finite...

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...

algebraic function. Examples of transcendental functions include the exponential function, the logarithm function, the hyperbolic functions, and the trigonometric...

differential operators. Special functions of mathematical physics, such as the trigonometric functions, the hypergeometric function and its generalizations...

In the physical sciences, the Airy function (or Airy function of the first kind) Ai(x) is a special function named after the British astronomer George...

domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends...

The hyperbolastic functions, also known as hyperbolastic growth models, are mathematical functions that are used in medical statistical modeling. These...

Floor and ceiling functions In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer...

Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its...

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving...

the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial...

analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions...

In mathematics and the field of transportation theory, the transport functions J(n,x) are defined by J ( n , x ) = ∫ 0 x t n e t ( e t − 1 ) 2 d t . {\displaystyle...

error functions. libcerf, numeric C library for complex error functions, provides the complex functions cerf, cerfc, cerfcx and the real functions erfi...

which in turn have many particular special functions as special cases, such as elementary functions, Bessel functions, and the classical orthogonal polynomials...