DLMF:6.7.E9 (Q2262)

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DLMF:6.7.E9
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    Statements

    test
    si ⁡ ( z ) = - ∫ 0 π / 2 e - z ⁢ cos ⁡ t ⁢ cos ⁡ ( z ⁢ sin ⁡ t ) ⁢ d t , shifted-sine-integral 𝑧 superscript subscript 0 𝜋 2 superscript 𝑒 𝑧 𝑡 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{si}\left(z\right)=-\int_{0}^{\pi/2}e^{-z% \cos t}\cos\left(z\sin t\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:6.7.E9
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
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    sine integral
    test
    si ⁡ ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E10.m2adec
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    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
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    Q11305
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1dec
    0 references
     
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