Concept

# Closed-form expression

Summary
In mathematics, an expression is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations (+, −, ×, ÷, and integer powers) and function composition. Commonly, the allowed functions are nth root, exponential function, logarithm, and trigonometric functions . However, the set of basic functions depends on the context. The closed-form problem arises when new ways are introduced for specifying mathematical objects, such as limits, series and integrals: given an object specified with such tools, a natural problem is to find, if possible, a closed-form expression of this object, that is, an expression of this object in terms of previous ways of specifying it. Example: roots of polynomials The quadratic formula :x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}. is a closed form of the solutions of the general quadratic equation ax^2+bx+c=0. More generally, in the context of polynomial equations,
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