DLMF:6.14.E6 (Q2304)

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DLMF:6.14.E6
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    Statements

    Defining formula
    ∫ 0 ∞ Ci 2 ⁡ ( t ) ⁢ d t = ∫ 0 ∞ si 2 ⁡ ( t ) ⁢ d t = 1 2 ⁢ π , superscript subscript 0 cosine-integral 2 𝑡 𝑡 superscript subscript 0 shifted-sine-integral 2 𝑡 𝑡 1 2 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}{\mathrm{Ci}^{2}}\left(t\right)% \mathrm{d}t=\int_{0}^{\infty}{\mathrm{si}^{2}}\left(t\right)\mathrm{d}t=\tfrac% {1}{2}\pi,}}
    0 references
    DLMF id
    DLMF:6.14.E6
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
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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.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
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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.m2abdec
    0 references
     
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