DLMF:7.2.E8 (Q2329)

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DLMF:7.2.E8
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    Statements

    test
    S ⁡ ( z ) = ∫ 0 z sin ⁡ ( 1 2 ⁢ π ⁢ t 2 ) ⁢ d t , Fresnel-sine-integral 𝑧 superscript subscript 0 𝑧 1 2 𝜋 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle S\left(z\right)=\int_{0}^{z}\sin\left(\tfrac{1}{2% }\pi t^{2}\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:7.2.E8
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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.m2afdec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
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    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
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    Q11312
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1gdec
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