Closed-form expression

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 ( $+, -, \times, /$ , and integer powers) and function composition. Commonly, the allowed functions are nth root, exponential function, logarithm, and trigonometric functions.^[1] 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.

^ Hyperbolic functions, inverse trigonometric functions and inverse hyperbolic functions are also allowed, since they can be expressed in terms of the preceding ones.

[1] Hyperbolic functions, inverse trigonometric functions and inverse hyperbolic functions are also allowed, since they can be expressed in terms of the preceding ones.

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