DLMF:4.35.E9 (Q1883)

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DLMF:4.35.E9
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    Statements

    Defining formula
    tanh ⁡ u ± tanh ⁡ v = sinh ⁡ ( u ± v ) cosh ⁡ u ⁢ cosh ⁡ v , plus-or-minus 𝑢 𝑣 plus-or-minus 𝑢 𝑣 𝑢 𝑣 {\displaystyle{\displaystyle\tanh u\pm\tanh v=\frac{\sinh\left(u\pm v\right)}{% \cosh u\cosh v},}}
    0 references
    DLMF id
    DLMF:4.35.E9
    0 references
    Symbols used
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2afdec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2aedec
    0 references
    hyperbolic tangent function
    Defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2aadec
    0 references
     
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