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单词 ElementaryFunction
释义

elementary function


An elementary functionMathworldPlanetmath is a real function (of one variable) that can be constructed by a finite number of elementary operations (additionPlanetmathPlanetmath, subtractionPlanetmathPlanetmath, multiplication and division) and compositions from constant functionsMathworldPlanetmath, the identity functionMathworldPlanetmath (xx), algebraic functionsMathworldPlanetmath, exponential functionsDlmfDlmfMathworldPlanetmath, logarithm functions, trigonometric functionsDlmfMathworldPlanetmath and cyclometric functions.

Examples

  • Consequently, the polynomial functions, the absolute valueMathworldPlanetmathPlanetmathPlanetmath|x|=x2,  the triangular-wave function  arcsin(sinx), the power functionDlmfDlmfPlanetmathxπ=eπlnx  and the function  xx=exlnx  are elementary functions (N.B., the real power functions entail that  x>0).

  • ζ(x):=n=11nx  and  Lix:=2xdtlnt  are not elementary functions — it may be shown that they can not be expressed is such a way which is required in the definition.

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更新时间:2025/5/4 18:59:21