In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x1/n).[1]
All elementary functions are continuous on their domains.
Elementary functions were introduced by Joseph Liouville in a series of papers from 1833 to 1841.[2][3][4] An algebraic treatment of elementary functions was started by Joseph Fels Ritt in the 1930s.[5] Many textbooks and dictionaries do not give a precise definition of the elementary functions, and mathematicians differ on it.[6]