DLMF:4.35.E22 (Q1896)

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DLMF:4.35.E22
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    Statements

    Defining formula
    tanh ⁡ z 2 = ( cosh ⁡ z - 1 cosh ⁡ z + 1 ) 1 / 2 = cosh ⁡ z - 1 sinh ⁡ z = sinh ⁡ z cosh ⁡ z + 1 . 𝑧 2 superscript 𝑧 1 𝑧 1 1 2 𝑧 1 𝑧 𝑧 𝑧 1 {\displaystyle{\displaystyle\tanh\frac{z}{2}=\left(\frac{\cosh z-1}{\cosh z+1}% \right)^{1/2}=\frac{\cosh z-1}{\sinh z}=\frac{\sinh z}{\cosh z+1}.}}
    0 references
    DLMF id
    DLMF:4.35.E22
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    Symbols used
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aodec
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    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2andec
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    hyperbolic tangent function
    Defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2acdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1edec
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