DLMF:9.10.E1 (Q2883)

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DLMF:9.10.E1
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    Statements

    Defining formula
    ∫ z ∞ Ai ⁡ ( t ) ⁢ d t = π ⁢ ( Ai ⁡ ( z ) ⁢ Gi ′ ⁡ ( z ) - Ai ′ ⁡ ( z ) ⁢ Gi ⁡ ( z ) ) , superscript subscript 𝑧 Airy-Ai 𝑡 𝑡 𝜋 Airy-Ai 𝑧 diffop Scorer-Gi 1 𝑧 diffop Airy-Ai 1 𝑧 Scorer-Gi 𝑧 {\displaystyle{\displaystyle\int_{z}^{\infty}\mathrm{Ai}\left(t\right)\mathrm{% d}t=\pi\left(\mathrm{Ai}\left(z\right)\mathrm{Gi}'\left(z\right)-\mathrm{Ai}'% \left(z\right)\mathrm{Gi}\left(z\right)\right),}}
    0 references
    DLMF id
    DLMF:9.10.E1
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1adec
    0 references
    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.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
     
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