DLMF:4.32.E4 (Q1857)

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DLMF:4.32.E4
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    Statements

    Defining formula
    arctan ⁡ x ≤ 1 2 ⁢ π ⁢ tanh ⁡ x , 𝑥 1 2 𝜋 𝑥 {\displaystyle{\displaystyle\operatorname{arctan}x\leq\tfrac{1}{2}\pi\tanh x,}}
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    DLMF id
    DLMF:4.32.E4
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    constraint
    x ≥ 0 𝑥 0 {\displaystyle{\displaystyle x\geq 0}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    hyperbolic tangent function
    Defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2aadec
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    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7adec
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    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1cdec
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