mathematics, elementary functions are those functions that are most commonly encountered by beginners. They are typically real functions of a single real...

class of elementary recursive functions ("Kalmár elementary functions") as a subset of the primitive recursive functions — specifically, those that can...

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. Equivalently, these...

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

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

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

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

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

}^{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...

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...

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...

Computable functions are the basic objects of study in computability theory. Informally, a function is computable if there is an algorithm that computes...

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...

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...

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,...

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

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...

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

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

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

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

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

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...

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

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

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

that the concept of elementary functions is merely conventional. If we redefine elementary functions to include the error function, then under this definition...