Closed Form Solution 308 浏览 0关注

In mathematics, an expression (mathematics)|expression is said to be a closed-form expression if it can be expressed analytically in terms of a finite set|finite number of certain well-known function (mathematics)|functions. Typically, these well-known functions are defined to be Elementary function (differential algebra)|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 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 Series (mathematics)#Infinite series|infinite series or continued fractions; neither includes integrals or limit of a sequence|limits. Indeed, by the Stone–Weierstrass theorem, any continuous function on the unit in...
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