DLMF:2.10.E21 (Q1008)

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DLMF:2.10.E21
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    Statements

    Defining formula
    cot ⁡ ( π ⁢ t ) 2 ⁢ i = - 1 2 - 1 e - 2 ⁢ π ⁢ i ⁢ t - 1 = 1 2 + 1 e 2 ⁢ π ⁢ i ⁢ t - 1 , 𝜋 𝑡 2 𝑖 1 2 1 superscript 𝑒 2 𝜋 𝑖 𝑡 1 1 2 1 superscript 𝑒 2 𝜋 𝑖 𝑡 1 {\displaystyle{\displaystyle\frac{\cot\left(\pi t\right)}{2i}=-\frac{1}{2}-% \frac{1}{e^{-2\pi it}-1}=\frac{1}{2}+\frac{1}{e^{2\pi it}-1},}}
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    DLMF id
    DLMF:2.10.E21
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2agdec
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