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

In recursion theory, an elementary recursive function, also called an elementary function, or a Kalmár elementary function, is a restricted form of a primitive...

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...

{\displaystyle {\mathsf {ELEMENTARY}}} consists of the decision problems that can be solved in time bounded by an elementary recursive function. The most quickly-growing...

basic functions, the functions that have a closed form are called elementary functions. The closed-form problem arises when new ways are introduced for...

}^{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...

antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function. A theorem by Liouville...

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...

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...

counter-domain, or set of destination of a function is a set into which all of the output of the function is constrained to fall. It is the set Y in the...

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

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}...

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...

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...

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,...

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...

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...

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

Elementary function Element (disambiguation) Elemental (disambiguation) This disambiguation page lists articles associated with the title Elementary. If an...

one must have either 11 or 12 elements. Elementary function – A kind of mathematical function Elementary function arithmetic – System of arithmetic in proof...

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

many elementary functions whose antiderivatives, even though they exist, cannot be expressed in terms of elementary functions. Elementary functions are...

reduce to an elementary function such as the natural logarithm or a rational function. In quantum statistics, the polylogarithm function appears as the...

sine function entirely. Constant problem – Problem of deciding whether an expression equals zero Elementary function – A kind of mathematical function Tarski's...

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

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