In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots...

branch of mathematical logic, elementary function arithmetic (EFA), also called elementary arithmetic and exponential function arithmetic, is the system of...

most functions that are encountered in elementary courses of mathematics are elementary in this sense, some elementary functions are not elementary for...

computational complexity theory, the complexity class ELEMENTARY of elementary recursive functions is the union of the classes E L E M E N T A R Y = ⋃ k...

in Borwein & Borwein. The elementary functions are constructed by composing arithmetic operations, the exponential function ( exp {\displaystyle \exp...

exponential function and polynomial roots. Functions that have a closed form for these basic functions are called elementary functions and include trigonometric...

of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed...

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

terms of elementary (Liouvillian) functions, the first published proof did not appear until 2008. There are countably many branches of the W function, denoted...

expressed as elementary functions. The antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions. These are...

when x is a positive integer, and no elementary function has this property, but a good solution is the gamma function f ( x ) = Γ ( x + 1 ) {\displaystyle...

In mathematics, an injective function (also known as injection, or one-to-one function ) is a function f that maps distinct elements of its domain to...

surjective function (also known as surjection, or onto function /ˈɒn.tuː/) is a function f such that, for every element y of the function's codomain, there...

}^{x}{\frac {e^{t}}{t}}\,dt.} The Risch algorithm shows that Ei is not an elementary function. The definition above can be used for positive values of x, but the...

sense that a function is computable if there exists an algorithm that can do the job of the function, i.e. given an input of the function domain it can...

procedure, because it is a method for deciding whether a function has an elementary function as an indefinite integral, and if it does, for determining...

In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom ⁡ ( f ) {\displaystyle \operatorname...

such one must have either 11 or 12 elements. Elementary function – Mathematical function Elementary function arithmetic – System of arithmetic in proof...

2005-02-07. mathlib on GitHub. "libultim – ultimate correctly-rounded elementary-function library". Archived from the original on 2021-03-01. "Git - glibc...

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function defined as: erf ⁡ z = 2 π ∫ 0 z e − t 2...

statistical mechanics, to find its partition function. Although no elementary function exists for the error function, as can be proven by the Risch algorithm...

science, arity (/ˈærɪti/ ) is the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank,...

switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the...

the sine function entirely. Constant problem – Problem of deciding whether an expression equals zero Elementary function – Mathematical function Tarski's...

the range of a function may refer to either of two closely related concepts: the codomain of the function, or the image of the function. In some cases...

the antiderivative of an elementary function is elementary and to compute the integral if is elementary. However, functions with closed expressions of...

one; however, unlike the operations before it, tetration is not an elementary function. The parameter a {\displaystyle a} is referred to as the base, while...

Liouvillian functions comprise a set of functions including the elementary functions and their repeated integrals. Liouvillian functions can be recursively...

in M. If N is an elementary substructure of M, then M is called an elementary extension of N. An embedding h: N → M is called an elementary embedding of N...

used interchangeably for such functions. Typical examples of analytic functions are The following elementary functions: All polynomials: if a polynomial...