DLMF:4.35.E36 (Q1910)

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DLMF:4.35.E36
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    Statements

    Defining formula
    tanh ⁡ z = sinh ⁡ ( 2 ⁢ x ) + i ⁢ sin ⁡ ( 2 ⁢ y ) cosh ⁡ ( 2 ⁢ x ) + cos ⁡ ( 2 ⁢ y ) , 𝑧 2 𝑥 𝑖 2 𝑦 2 𝑥 2 𝑦 {\displaystyle{\displaystyle\tanh z=\frac{\sinh\left(2x\right)+i\sin\left(2y% \right)}{\cosh\left(2x\right)+\cos\left(2y\right)},}}
    0 references
    DLMF id
    DLMF:4.35.E36
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aydec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2axdec
    0 references
    hyperbolic tangent function
    Defining formula
    tanh ⁡ z 𝑧 {\displaystyle{\displaystyle\tanh\NVar{z}}}
    xml-id
    C4.S28.E4.m2agdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1bdec
    0 references
    Q11222
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1bdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1sdec
    0 references
     
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