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- Closed-form_expression abstract "In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a finite number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions—constants, one variable x, elementary operations of arithmetic (+ − × ÷), nth roots, exponent and logarithm (which thus also include trigonometric functions and inverse trigonometric functions). Often problems are said to be tractable if they can be solved in terms of a closed-form expression.Closed–form expressions are an important sub-class of analytic expressions, which contain a bounded or unbounded number of applications of well-known functions. Unlike the broader analytic expressions, the closed-form expressions do not include infinite series or continued fractions; neither includes integrals or limits. Indeed, by the Stone–Weierstrass theorem, any continuous function on the unit interval can be expressed as a limit of polynomials, so any class of functions containing the polynomials and closed under limits will necessarily include all continuous functions.Similarly, an equation or system of equations is said to have a closed-form solution if, and only if, at least one solution can be expressed as a closed-form expression; and it is said to have an analytic solution if and only if at least one solution can be expressed as an analytic expression. There is a subtle distinction between a "closed-form function" and a "closed-form number" in the discussion of a "closed-form solution", discussed in (Chow 1999) and below. A closed-form or analytic solution is sometimes referred to as an explicit solution.An area of study in mathematics referred to broadly as Galois theory involves proving that no closed-form expression exists in certain contexts, based on the central example of closed-form solutions to polynomials.Equations or systems too complex for closed-form or analytical solutions can often be analysed by mathematical modelling and computer simulation.".
- Closed-form_expression wikiPageID "585143".
- Closed-form_expression wikiPageRevisionID "593798562".
- Closed-form_expression hasPhotoCollection Closed-form_expression.
- Closed-form_expression title "Closed-Form Solution".
- Closed-form_expression urlname "Closed-FormSolution".
- Closed-form_expression subject Category:Algebra.
- Closed-form_expression subject Category:Special_functions.
- Closed-form_expression type Abstraction100002137.
- Closed-form_expression type Function113783816.
- Closed-form_expression type MathematicalRelation113783581.
- Closed-form_expression type Relation100031921.
- Closed-form_expression type SpecialFunctions.
- Closed-form_expression comment "In mathematics, an expression is said to be a closed-form expression if it can be expressed analytically in terms of a finite number of certain "well-known" functions. Typically, these well-known functions are defined to be elementary functions—constants, one variable x, elementary operations of arithmetic (+ − × ÷), nth roots, exponent and logarithm (which thus also include trigonometric functions and inverse trigonometric functions).".
- Closed-form_expression label "Closed-form expression".
- Closed-form_expression label "Forma cerrada (matemática)".
- Closed-form_expression label "Forma fechada (matemática)".
- Closed-form_expression label "Solution de forme fermée".
- Closed-form_expression label "Wzór jawny".
- Closed-form_expression label "解析解".
- Closed-form_expression sameAs Analytické_řešení.
- Closed-form_expression sameAs Forma_cerrada_(matemática).
- Closed-form_expression sameAs Solution_de_forme_fermée.
- Closed-form_expression sameAs Wzór_jawny.
- Closed-form_expression sameAs Forma_fechada_(matemática).
- Closed-form_expression sameAs m.02sljs.
- Closed-form_expression sameAs Q777407.
- Closed-form_expression sameAs Q777407.
- Closed-form_expression sameAs Closed-form_expression.
- Closed-form_expression wasDerivedFrom Closed-form_expression?oldid=593798562.
- Closed-form_expression isPrimaryTopicOf Closed-form_expression.