DLMF:13.6.E11 (Q4398)

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DLMF:13.6.E11
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    Statements

    Defining formula
    U ⁡ ( 5 6 , 5 3 , 4 3 ⁢ z 3 / 2 ) = π ⁢ 3 5 / 6 ⁢ exp ⁡ ( 2 3 ⁢ z 3 / 2 ) 2 2 / 3 ⁢ z ⁢ Ai ⁡ ( z ) . Kummer-confluent-hypergeometric-U 5 6 5 3 4 3 superscript 𝑧 3 2 𝜋 superscript 3 5 6 2 3 superscript 𝑧 3 2 superscript 2 2 3 𝑧 Airy-Ai 𝑧 {\displaystyle{\displaystyle U\left(\tfrac{5}{6},\tfrac{5}{3},\tfrac{4}{3}z^{3% /2}\right)=\sqrt{\pi}\frac{3^{5/6}\exp\left(\tfrac{2}{3}z^{3/2}\right)}{2^{2/3% }z}\mathrm{Ai}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.6.E11
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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.m1adec
    0 references
    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2aedec
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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.m2acdec
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    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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