DLMF:4.21.E40 (Q1744)

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DLMF:4.21.E40
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    Statements

    test
    cot ⁡ z = sin ⁡ ( 2 ⁢ x ) - i ⁢ sinh ⁡ ( 2 ⁢ y ) cosh ⁡ ( 2 ⁢ y ) - cos ⁡ ( 2 ⁢ x ) . 𝑧 2 𝑥 imaginary-unit 2 𝑦 2 𝑦 2 𝑥 {\displaystyle{\displaystyle\cot z=\frac{\sin\left(2x\right)-\mathrm{i}\sinh% \left(2y\right)}{\cosh\left(2y\right)-\cos\left(2x\right)}.}}
    0 references
    DLMF id
    DLMF:4.21.E40
    0 references
    Symbols used
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aabdec
    0 references
    cotangent function
    test
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2addec
    0 references
    hyperbolic cosine function
    test
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2acdec
    0 references
     
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