In mathematics, an elementary function is a function of one variable built from a finite number of exponentials, logarithms, constants, and nth roots through composition and combinations using the four elementary operations (+ – × ÷). By allowing these functions (and constants) to be complex numbers, trigonometric functions and their inverses become included in the elementary functions (see trigonometric functions and complex exponentials).
The roots of equations are the functions implicitly defined as solving a polynomial equation with constant coefficients. For polynomials of degree four and smaller there are explicit formulae for the roots (the formulae are elementary functions).
Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841. An algebraic treatment of elementary functions was started by Joseph Fels Ritt in the 1930s.
Read more about Elementary Function: Examples, Differential Algebra
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