DLMF:9.12.E21 (Q2949)

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DLMF:9.12.E21
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    Statements

    Defining formula
    Gi ⁡ ( z ) = - 1 π ⁢ ∫ 0 ∞ exp ⁡ ( - 1 3 ⁢ t 3 - 1 2 ⁢ z ⁢ t ) ⁢ cos ⁡ ( 1 2 ⁢ 3 ⁢ z ⁢ t + 2 3 ⁢ π ) ⁢ d t . Scorer-Gi 𝑧 1 𝜋 superscript subscript 0 1 3 superscript 𝑡 3 1 2 𝑧 𝑡 1 2 3 𝑧 𝑡 2 3 𝜋 𝑡 {\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=-\frac{1}{\pi}\int_{0}^{% \infty}\exp\left(-\tfrac{1}{3}t^{3}-\tfrac{1}{2}zt\right)\cos\left(\tfrac{1}{2% }\sqrt{3}zt+\tfrac{2}{3}\pi\right)\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:9.12.E21
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    Symbols used
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2aldec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
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    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
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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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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aadec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
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    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1qdec
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