DLMF:4.35.E26 (Q1900)

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DLMF:4.35.E26
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    Statements

    Defining formula
    sinh ⁡ ( 2 ⁢ z ) = 2 ⁢ sinh ⁡ z ⁢ cosh ⁡ z = 2 ⁢ tanh ⁡ z 1 - tanh 2 ⁡ z , 2 𝑧 2 𝑧 𝑧 2 𝑧 1 2 𝑧 {\displaystyle{\displaystyle\sinh\left(2z\right)=2\sinh z\cosh z=\frac{2\tanh z% }{1-{\tanh^{2}}z},}}
    0 references
    DLMF id
    DLMF:4.35.E26
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    Symbols used
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aqdec
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    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2apdec
    0 references
    hyperbolic tangent function
    Defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2aedec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1idec
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