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DLMF:6.15.E2 - MaRDI portal

DLMF:6.15.E2 (Q3005)

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DLMF:6.15.E2
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    Statements

    DLMF defining formula
    ∑ n = 1 ∞ si ⁡ ( π ⁢ n ) n = 1 2 ⁢ π ⁢ ( ln ⁡ π - 1 ) , superscript subscript 𝑛 1 shifted-sine-integral 𝜋 𝑛 𝑛 1 2 𝜋 𝜋 1 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\frac{\mathrm{si}\left(\pi n% \right)}{n}=\tfrac{1}{2}\pi(\ln\pi-1),}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    sine integral
    DLMF defining formula
    si ⁡ ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E10.m2adec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1adec
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    Identifiers

     
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