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DLMF:4.35.E22 - MaRDI portal

DLMF:4.35.E22 (Q2273)

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DLMF:4.35.E22
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    Statements

    DLMF 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
    Symbols used
    hyperbolic cosine function
    DLMF defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aodec
    0 references
    hyperbolic sine function
    DLMF defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2andec
    0 references
    hyperbolic tangent function
    DLMF defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2acdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1edec
    0 references

    Identifiers

     
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