Transcendental equation

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In applied mathematics, a transcendental equation is an equation over the real (or complex) numbers that is not algebraic, that is, if at least one of its sides describes a transcendental function.^[1] Examples include:

${\displaystyle {\begin{aligned}x&=e^{-x}\\x&=\cos x\\2^{x}&=x^{2}\end{aligned}}}$

A transcendental equation need not be an equation between elementary functions, although most published examples are.

In some cases, a transcendental equation can be solved by transforming it into an equivalent algebraic equation. Some such transformations are sketched below; computer algebra systems may provide more elaborated transformations.^[a]

In general, however, only approximate solutions can be found.^[2]

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