DLMF:4.35.E39 (Q1913)

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DLMF:4.35.E39
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    Statements

    Defining formula
    | cosh ⁡ z | = ( sinh 2 ⁡ x + cos 2 ⁡ y ) 1 / 2 = ( 1 2 ⁢ ( cosh ⁡ ( 2 ⁢ x ) + cos ⁡ ( 2 ⁢ y ) ) ) 1 / 2 , 𝑧 superscript 2 𝑥 2 𝑦 1 2 superscript 1 2 2 𝑥 2 𝑦 1 2 {\displaystyle{\displaystyle|\cosh z|=({\sinh^{2}}x+{\cos^{2}}y)^{1/2}=\left(% \tfrac{1}{2}(\cosh\left(2x\right)+\cos\left(2y\right))\right)^{1/2},}}
    0 references
    DLMF id
    DLMF:4.35.E39
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    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aedec
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    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aabdec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2aaadec
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    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1edec
    0 references
    Q11222
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1edec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1vdec
    0 references
     
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