Concept

Elementary function

Summary
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, including possibly their inverse functions (e.g., arcsin, log, or x1/n). All elementary functions are continuous on their domains. 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. Examples Basic examples Elementary functions of a single variable x include:
  • Constant functions: 2,\ \pi,\ e, etc.
  • Rational powers of x: x,\ x^2,\ \sqrt{x}\ (x^\frac{1}{2}),\ x^\frac{2}{3}, etc.
  • Exponential functions: e^x, \ a^x
  • Logarithms: \ln x, \ \log_a x
  • Trigonometric functions: \sin x,\ \c
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