DLMF:9.11.E15 (Q2922)

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DLMF:9.11.E15
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    Statements

    test
    ∫ 0 ∞ t α - 1 ⁢ Ai 2 ⁡ ( t ) ⁢ d t = 2 ⁢ Γ ⁡ ( α ) π 1 / 2 ⁢ 12 ( 2 ⁢ α + 5 ) / 6 ⁢ Γ ⁡ ( 1 3 ⁢ α + 5 6 ) , superscript subscript 0 superscript 𝑡 𝛼 1 Airy-Ai 2 𝑡 𝑡 2 Euler-Gamma 𝛼 superscript 𝜋 1 2 superscript 12 2 𝛼 5 6 Euler-Gamma 1 3 𝛼 5 6 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{\alpha-1}{\mathrm{Ai}^{2}}% \left(t\right)\mathrm{d}t=\frac{2\Gamma\left(\alpha\right)}{\pi^{1/2}12^{(2% \alpha+5)/6}\Gamma\left(\frac{1}{3}\alpha+\frac{5}{6}\right)},}}
    0 references
    DLMF id
    DLMF:9.11.E15
    0 references
    constraint
    ℜ ⁡ α > 0 𝛼 0 {\displaystyle{\displaystyle\Re\alpha>0}}
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    Symbols used
    Q10919
    test
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1afdec
    0 references
     
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