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transcendental equation : ウィキペディア英語版
transcendental equation

A transcendental equation is an equation containing a transcendental function of the variable(s) being solved for. Such equations often do not have closed-form solutions. Examples include:
:\begin
x &= e^ \\
x &= \cos x
\end
==Solvable transcendental equations==

Equations where the variable to be solved for appears only once, as an argument to the transcendental function, are easily solvable with inverse functions; similarly if the equation can be factored or transformed to such a case:
/ 3 + \pi/6 (for m, n integers)
|}
Some transcendental equations can be shown to have no real solution, or to have only trivial solutions.
Some can be solved because they are compositions of algebraic functions with transcendental functions.
But most equations where the variable appears both as an argument to a transcendental function and elsewhere in the equation are not solvable in closed form.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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