An elementary function is a real function (of one variable) that can be constructed by a finite number of elementary operations (addition, subtraction, multiplication and division) and compositions from constant functions, the identity function (xx), algebraic functions, exponential functions, logarithm functions, trigonometric functions and cyclometric functions.

Examples

• Consequently, the polynomial functions, the absolute value |x| = , the triangular-wave function arcsin(sin x), the power function x^π = e^{π ln x} and the function x^x = e^{x ln x} are elementary functions (N.B., the real power functions entail that x > 0).
• ζ(x) := ∑ _n=1^∞ and Li x := ∫ ₂^x are not elementary functions — it may be shown that they can not be expressed is such a way which is required in the definition.