DLMF:9.10.E18 (Q2901)

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DLMF:9.10.E18
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    Statements

    Defining formula
    Ai ⁡ ( z ) = 3 ⁢ z 5 / 4 ⁢ e - ( 2 / 3 ) ⁢ z 3 / 2 4 ⁢ π ⁢ ∫ 0 ∞ t - 3 / 4 ⁢ e - ( 2 / 3 ) ⁢ t 3 / 2 ⁢ Ai ⁡ ( t ) z 3 / 2 + t 3 / 2 ⁢ d t , Airy-Ai 𝑧 3 superscript 𝑧 5 4 superscript 𝑒 2 3 superscript 𝑧 3 2 4 𝜋 superscript subscript 0 superscript 𝑡 3 4 superscript 𝑒 2 3 superscript 𝑡 3 2 Airy-Ai 𝑡 superscript 𝑧 3 2 superscript 𝑡 3 2 𝑡 {\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{3z^{5/4}e^{-(2/3)z% ^{3/2}}}{4\pi}\*\int_{0}^{\infty}\frac{t^{-3/4}e^{-(2/3)t^{3/2}}\mathrm{Ai}% \left(t\right)}{z^{3/2}+t^{3/2}}\mathrm{d}t,}}
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    DLMF id
    DLMF:9.10.E18
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    constraint
    | ph ⁡ z | < 2 3 ⁢ π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{2}{3}\pi}}
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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.m2agdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aqdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aqdec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
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    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1fdec
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