DLMF:6.15.E3 (Q2308)

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DLMF:6.15.E3
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    Statements

    test
    ∑ n = 1 ∞ ( - 1 ) n ⁢ Ci ⁡ ( 2 ⁢ π ⁢ n ) = 1 - ln ⁡ 2 - 1 2 ⁢ γ , superscript subscript 𝑛 1 superscript 1 𝑛 cosine-integral 2 𝜋 𝑛 1 2 1 2 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}(-1)^{n}\mathrm{Ci}\left(2\pi n% \right)=1-\ln 2-\tfrac{1}{2}\gamma,}}
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    DLMF id
    DLMF:6.15.E3
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    Symbols used
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2aadec
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    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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    cosine integral
    test
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2aadec
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    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
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    Q11308
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1bdec
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