DLMF:9.10.E20 (Q3603)

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DLMF:9.10.E20
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    Statements

    DLMF defining formula
    ∫ 0 x ∫ 0 v Ai ⁡ ( t ) ⁢ d t ⁢ d v = x ⁢ ∫ 0 x Ai ⁡ ( t ) ⁢ d t - Ai ′ ⁡ ( x ) + Ai ′ ⁡ ( 0 ) , superscript subscript 0 𝑥 superscript subscript 0 𝑣 Airy-Ai 𝑡 𝑡 𝑣 𝑥 superscript subscript 0 𝑥 Airy-Ai 𝑡 𝑡 diffop Airy-Ai 1 𝑥 diffop Airy-Ai 1 0 {\displaystyle{\displaystyle\int_{0}^{x}\!\!\int_{0}^{v}\mathrm{Ai}\left(t% \right)\mathrm{d}t\mathrm{d}v=x\int_{0}^{x}\mathrm{Ai}\left(t\right)\mathrm{d}% t-\mathrm{Ai}'\left(x\right)+\mathrm{Ai}'\left(0\right),}}
    0 references
    Symbols used
    Q10893
    DLMF defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1akdec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1asdec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ardec
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    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1edec
    0 references
    parameter
    DLMF defining formula
    v 𝑣 {\displaystyle{\displaystyle v}}
    xml-id
    C9.S10.XMD4.m1dec
    0 references

    Identifiers

     
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