DLMF:9.10.E17 (Q2900)

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DLMF:9.10.E17
No description defined

    Statements

    Defining formula
    ∫ 0 ∞ t α - 1 ⁢ Ai ⁡ ( t ) ⁢ d t = Γ ⁡ ( α ) 3 ( α + 2 ) / 3 ⁢ Γ ⁡ ( 1 3 ⁢ α + 2 3 ) , superscript subscript 0 superscript 𝑡 𝛼 1 Airy-Ai 𝑡 𝑡 Euler-Gamma 𝛼 superscript 3 𝛼 2 3 Euler-Gamma 1 3 𝛼 2 3 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{\alpha-1}\mathrm{Ai}\left(t% \right)\mathrm{d}t=\frac{\Gamma\left(\alpha\right)}{3^{(\alpha+2)/3}\Gamma% \left(\tfrac{1}{3}\alpha+\tfrac{2}{3}\right)},}}
    0 references
    DLMF id
    DLMF:9.10.E17
    0 references
    constraint
    ℜ ⁡ α > 0 𝛼 0 {\displaystyle{\displaystyle\Re\alpha>0}}
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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.m1ahdec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1apdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3apdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1acdec
    0 references
     
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