Elementary function

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 x^1/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]

^ Spivak, Michael. (1994). Calculus (3rd ed.). Houston, Tex.: Publish or Perish. p. 359. ISBN 0914098896. OCLC 31441929.
^ Liouville 1833a.
^ Liouville 1833b.
^ Liouville 1833c.
^ Ritt 1950.
^ Subbotin, Igor Ya.; Bilotskii, N. N. (March 2008). "Algorithms and Fundamental Concepts of Calculus" (PDF). Journal of Research in Innovative Teaching. 1 (1): 82–94.

[1] Spivak, Michael. (1994). Calculus (3rd ed.). Houston, Tex.: Publish or Perish. p. 359. ISBN 0914098896. OCLC 31441929.

[2] Liouville 1833a.

[3] Liouville 1833b.

[4] Liouville 1833c.

[5] Ritt 1950.

[:0-6] Subbotin, Igor Ya.; Bilotskii, N. N. (March 2008). "Algorithms and Fundamental Concepts of Calculus" (PDF). Journal of Research in Innovative Teaching. 1 (1): 82–94.

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