DLMF:4.21.E43 (Q1747)

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DLMF:4.21.E43
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    Statements

    Defining formula
    | tan ⁡ z | = ( cosh ⁡ ( 2 ⁢ y ) - cos ⁡ ( 2 ⁢ x ) cosh ⁡ ( 2 ⁢ y ) + cos ⁡ ( 2 ⁢ x ) ) 1 / 2 . 𝑧 superscript 2 𝑦 2 𝑥 2 𝑦 2 𝑥 1 2 {\displaystyle{\displaystyle|\tan z|=\left(\frac{\cosh\left(2y\right)-\cos% \left(2x\right)}{\cosh\left(2y\right)+\cos\left(2x\right)}\right)^{1/2}.}}
    0 references
    DLMF id
    DLMF:4.21.E43
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aaedec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2afdec
    0 references
    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2aidec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1fdec
    0 references
     
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