Formulable

Formulable is an adjective used to describe something that can be expressed or described by a formula—a finite, symbolic expression built from a prescribed set of operations and symbols. In mathematics and related disciplines, a relation, function, sequence, or constant is formulable if there exists such a formula that computes its value from given inputs.

In mathematics, many objects are formulable: polynomials, rational functions, exponentials, logarithms, and trigonometric expressions can all be written as explicit formulas. Some functions have finite closed-form expressions or representations using standard elementary or special functions. However, there are objects that lack a single finite formula; definitions by recursion, piecewise rules, or numerical procedures may be required, making them non-formulable in the strict sense.

In computing and symbolic mathematics, formulable expressions are those that can be manipulated by algebraic rules. Software for symbolic computation treats formulable expressions with operations such as simplification, expansion, and differentiation, while non-formulable definitions may require procedural algorithms or numerical approximation.

Etymology and nuance: Formulable comes from form + able, indicating the ability to be expressed as a formula. In some mathematical contexts, formulable is used interchangeably with expressible, though closed-form denotes a stronger category of explicit formulas.

See also: formula; closed form; symbolic computation; recursion; piecewise function.