expressible in closed form

An expression is , if it can be converted (simplified) into an expression containing only elementary functionsMathworldPlanetmath, combined by a finite amount of rational operationsMathworldPlanetmath and compositions. Thus, such a closed formMathworldPlanetmath must not e.g. limit signs, integral signs, sum signs and “…”.

For example,


may be expressed in the closed form


but for


there exists no closed form.

In certain contexts, the of the “elementary functions” may be enlarged by allowing in it some other functions, e.g. the error functionDlmfDlmfPlanetmath.

Title expressible in closed form
Canonical name ExpressibleInClosedForm
Date of creation 2013-03-22 18:29:09
Last modified on 2013-03-22 18:29:09
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 8
Author pahio (2872)
Entry type Definition
Classification msc 30A99
Classification msc 26E99
Related topic ClosedForm
Related topic IrreducibilityOfBinomialsWithUnityCoefficients
Related topic ReductionOfEllipticIntegralsToStandardForm
Defines closed form