DLMF:6.2.E10 (Q2220)

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DLMF:6.2.E10
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    Statements

    test
    si ⁡ ( z ) = - ∫ z ∞ sin ⁡ t t ⁢ d t = Si ⁡ ( z ) - 1 2 ⁢ π . shifted-sine-integral 𝑧 superscript subscript 𝑧 𝑡 𝑡 𝑡 sine-integral 𝑧 1 2 𝜋 {\displaystyle{\displaystyle\mathrm{si}\left(z\right)=-\int_{z}^{\infty}\frac{% \sin t}{t}\mathrm{d}t=\mathrm{Si}\left(z\right)-\tfrac{1}{2}\pi.}}
    0 references
    DLMF id
    DLMF:6.2.E10
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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    sine integral
    test
    Si ⁡ ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E9.m2aadec
    0 references
    Q11305
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1edec
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