Transcendental equation

Transcendental equation

A transcendental equation is an equation containing a transcendental function. Examples of such an equation are

:x = e^{-x} :x = sin (x)

olution methods

Some methods of finding solutions to a transcendental equation use graphical or numerical methods. For a graphical solution, one method is to set each side of a single variable transcendental equation equal to a dependent variable (for example, y) and plot the two graphs, using their intersecting points to find solutions. The numerical solution extends from finding the point at which the intersections occur using some kind of numerical calculations (calculator or math software). Approximations can also be made by truncating the Taylor series if the variable is considered to be small. Additionally, Newton%27s method could be used to solve the equation.

Often special functions can be used to write the solutions to transcendental equations in closed form. In particular, the first equation has a solution in terms of the Lambert W Function.

See also

*Transcendental number
*Lambert W Function


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  • 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 equation — noun : an equation containing transcendental functions of the unknowns * * * Math. an equation that involves transcendental functions …   Useful english dictionary

  • transcendental equation — Math. an equation that involves transcendental functions. * * * …   Universalium

  • 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 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

  • Equation — E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the night.… …   The Collaborative International Dictionary of English

  • Equation box — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… …   The Collaborative International Dictionary of English

  • Equation clock — Equation E*qua tion, n. [L. aequatio an equalizing: cf. F. [ e]quation equation. See {Equate}.] 1. A making equal; equal division; equality; equilibrium. [1913 Webster] Again the golden day resumed its right, And ruled in just equation with the… …   The Collaborative International Dictionary of English

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