DLMF:9.11.E18 (Q2925)

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DLMF:9.11.E18
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    Statements

    Defining formula
    ∫ 0 ∞ Ai 4 ⁡ ( t ) ⁢ d t = ln ⁡ 3 24 ⁢ π 2 . superscript subscript 0 Airy-Ai 4 𝑡 𝑡 3 24 superscript 𝜋 2 {\displaystyle{\displaystyle\int_{0}^{\infty}{\mathrm{Ai}^{4}}\left(t\right)% \mathrm{d}t=\frac{\ln 3}{24\pi^{2}}.}}
    0 references
    DLMF id
    DLMF:9.11.E18
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    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1aidec
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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.m2aidec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aodec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aodec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
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