DLMF:4.15.E2 (Q1664)

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DLMF:4.15.E2
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    Statements

    test
    cot ⁡ ( x + i ⁢ y ) = - tan ⁡ ( x + 1 2 ⁢ π + i ⁢ y ) , 𝑥 𝑖 𝑦 𝑥 1 2 𝜋 𝑖 𝑦 {\displaystyle{\displaystyle\cot\left(x+iy\right)=-\tan\left(x+\tfrac{1}{2}\pi% +iy\right),}}
    0 references
    DLMF id
    DLMF:4.15.E2
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    cotangent function
    test
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2aadec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
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    tangent function
    test
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2abdec
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    Q11218
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1mdec
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    Q11222
    test
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1gdec
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