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mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph...

In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. The exponential...

\{a_{i}\},\{b_{i}\}} of constants or functions. From the perspective of number theory, these are called generalized continued fraction. From the perspective...

mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of...

The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic...

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function e r f : C → C {\displaystyle \mathrm {erf}...

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...

may also be useful. Lung transplantation may be an option if lung function continues to worsen. Pancreatic enzyme replacement and fat-soluble vitamin supplementation...

generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often...

Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions...

"Irrationality and transcendence of values of special functions" (PDF). Amoretti, F. (1855). "Sur la fraction continue [0,1,2,3,4,...]". Nouvelles annales de mathématiques...

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

mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...

In mathematics, Minkowski's question-mark function, denoted ?(x), is a function with unusual fractal properties, defined by Hermann Minkowski in 1904...

field theory, the Wightman distributions can be analytically continued to analytic functions in Euclidean space with the domain restricted to ordered n-tuples...

A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac...

In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood...

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...

In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse...

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