DLMF:4.40.E4 (Q1976)

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DLMF:4.40.E4
No description defined

    Statements

    Defining formula
    ∫ csch ⁡ x ⁢ d x = ln ⁡ ( tanh ⁡ ( 1 2 ⁢ x ) ) , 𝑥 𝑥 1 2 𝑥 {\displaystyle{\displaystyle\int\operatorname{csch}x\mathrm{d}x=\ln\left(\tanh% \left(\tfrac{1}{2}x\right)\right),}}
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    DLMF id
    DLMF:4.40.E4
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    constraint
    0 < x < ∞ 0 𝑥 {\displaystyle{\displaystyle 0<x<\infty}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
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    hyperbolic cosecant function
    Defining formula
    csch ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{csch}\NVar{z}}}
    xml-id
    C4.S28.E5.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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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1cdec
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