# transcendental function

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transcendental function
a function that is not an algebraic function.
[1875-80]

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In mathematics, a function not expressible as a finite combination of the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extracting a root.

Examples include the functions log x, sin x, cos x, ex and any functions containing them. Such functions are expressible in algebraic terms only as infinite series. In general, the term transcendental means nonalgebraic. See also transcendental number.

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Universalium. 2010.

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• Transcendental function — Transcendental Tran scen*den tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster] 2. (Philos.) In the Kantian system, of or pertaining to that which can be… …   The Collaborative International Dictionary of English

• Transcendental function — A transcendental function is a function that does not satisfy a polynomial equation whose coefficients are themselves polynomials, in contrast to an algebraic function, which does satisfy such an equation. In other words a transcendental function …   Wikipedia

• transcendental function — Math. a function that is not an algebraic function. [1875 80] * * * transcendental function noun (mathematics) Any function that cannot be defined by a finite number of algebraic operations • • • Main Entry: ↑transcend …   Useful english dictionary

• transcendental function — noun a function which does not satisfy a polynomial equation whose coefficients are themselves polynomials …   Wiktionary

• Transcendental — Tran scen*den tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster] 2. (Philos.) In the Kantian system, of or pertaining to that which can be determined a… …   The Collaborative International Dictionary of English

• Transcendental curve — Transcendental Tran scen*den tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster] 2. (Philos.) In the Kantian system, of or pertaining to that which can be… …   The Collaborative International Dictionary of English

• Transcendental equation — Transcendental Tran scen*den tal, a. [Cf. F. transcendantal, G. transcendental.] 1. Supereminent; surpassing others; as, transcendental being or qualities. [1913 Webster] 2. (Philos.) In the Kantian system, of or pertaining to that which can be… …   The Collaborative International Dictionary of English

• Transcendental functions — Function Func tion, n. [L. functio, fr. fungi to perform, execute, akin to Skr. bhuj to enjoy, have the use of: cf. F. fonction. Cf. {Defunct}.] 1. The act of executing or performing any duty, office, or calling; performance. In the function of… …   The Collaborative International Dictionary of English

• Function — Func tion, n. [L. functio, fr. fungi to perform, execute, akin to Skr. bhuj to enjoy, have the use of: cf. F. fonction. Cf. {Defunct}.] 1. The act of executing or performing any duty, office, or calling; performance. In the function of his public …   The Collaborative International Dictionary of English

• Transcendental — can refer to:In mathematics: * Transcendental number, a class of irrational numbers * Transcendental function, a class of functionsIn philosophy and religion: * Transcendence (philosophy) * Transcendental idealism, a philosophical doctrine… …   Wikipedia