DLMF:6.15.E1 (Q2306)

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DLMF:6.15.E1
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    Statements

    Defining formula
    ∑ n = 1 ∞ Ci ⁡ ( π ⁢ n ) = 1 2 ⁢ ( ln ⁡ 2 - γ ) , superscript subscript 𝑛 1 cosine-integral 𝜋 𝑛 1 2 2 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\mathrm{Ci}\left(\pi n\right)=% \tfrac{1}{2}(\ln 2-\gamma),}}
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    DLMF id
    DLMF:6.15.E1
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    Symbols used
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosine integral
    Defining formula
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2adec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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    Q11308
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1dec
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