DLMF:6.14.E5 (Q2303)

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DLMF:6.14.E5
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    Statements

    Defining formula
    ∫ 0 ∞ cos ⁡ t ⁢ Ci ⁡ ( t ) ⁢ d t = ∫ 0 ∞ sin ⁡ t ⁢ si ⁡ ( t ) ⁢ d t = - 1 4 ⁢ π , superscript subscript 0 𝑡 cosine-integral 𝑡 𝑡 superscript subscript 0 𝑡 shifted-sine-integral 𝑡 𝑡 1 4 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}\cos t\mathrm{Ci}\left(t\right)% \mathrm{d}t=\int_{0}^{\infty}\sin t\mathrm{si}\left(t\right)\mathrm{d}t=-% \tfrac{1}{4}\pi,}}
    0 references
    DLMF id
    DLMF:6.14.E5
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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.m2adec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.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.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
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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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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
     
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