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...

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

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...

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

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

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...

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

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...

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

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...

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

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

Langevin functions are a pair of special functions that appear when studying an idealized paramagnetic material in statistical mechanics. These functions are...

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

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

holonomic function is an element of a holonomic module of smooth functions. Holonomic functions can also be described as differentiably finite functions, also...

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

data for special functions and their applications. It is intended as an update of Abramowitz's and Stegun's Handbook of Mathematical Functions (A&S). It...

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

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

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...

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

functions and eponyms List of types of functions Polynomial Rational function Special functions Transcendental function Ahlfors, Lars (1979). Complex Analysis...

arguments. The even and odd functions satisfy by definition simple reflection relations around a = 0. For all even functions, f ( − x ) = f ( x ) , {\displaystyle...

rules for computing the derivative of a function in calculus. Unless otherwise stated, all functions are functions of real numbers ( R {\textstyle \mathbb...

asymptotic analysis, special functions, and numerical analysis. He was the editor in chief of the NIST Digital Library of Mathematical Functions. 1969: Silver...

influential in the study of special functions and their associated differential equations as well as in the study of functions of complex variables. Whittaker's...

In mathematics, the Mittag-Leffler functions are a family of special functions. They are complex-valued functions of a complex argument z, and moreover...