DLMF:6.15.E4 (Q2309)

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DLMF:6.15.E4
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    Statements

    Defining formula
    ∑ n = 1 ∞ ( - 1 ) n ⁢ si ⁡ ( 2 ⁢ π ⁢ n ) n = π ⁢ ( 3 2 ⁢ ln ⁡ 2 - 1 ) . superscript subscript 𝑛 1 superscript 1 𝑛 shifted-sine-integral 2 𝜋 𝑛 𝑛 𝜋 3 2 2 1 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}(-1)^{n}\frac{\mathrm{si}\left(% 2\pi n\right)}{n}=\pi(\tfrac{3}{2}\ln 2-1).}}
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    DLMF id
    DLMF:6.15.E4
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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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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
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    sine integral
    Defining formula
    si ⁡ ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E10.m2aadec
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