DLMF:4.26.E13 (Q1829)

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DLMF:4.26.E13
No description defined

    Statements

    Defining formula
    ∫ 0 ∞ sin ⁡ ( t 2 ) ⁢ d t = ∫ 0 ∞ cos ⁡ ( t 2 ) ⁢ d t = 1 2 ⁢ π 2 . superscript subscript 0 superscript 𝑡 2 𝑡 superscript subscript 0 superscript 𝑡 2 𝑡 1 2 𝜋 2 {\displaystyle{\displaystyle\int_{0}^{\infty}\sin\left(t^{2}\right)\mathrm{d}t% =\int_{0}^{\infty}\cos\left(t^{2}\right)\mathrm{d}t=\frac{1}{2}\sqrt{\frac{\pi% }{2}}.}}
    0 references
    DLMF id
    DLMF:4.26.E13
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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.m2ahdec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2agdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2ahdec
    0 references
     
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