DLMF:9.8.E10 (Q2842)

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DLMF:9.8.E10
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    Statements

    Defining formula
    | x | - 1 / 2 ⁢ N 2 ⁡ ( x ) = 1 2 ⁢ ξ ⁢ ( J 2 / 3 2 ⁡ ( ξ ) + Y 2 / 3 2 ⁡ ( ξ ) ) , superscript 𝑥 1 2 modulus-Airy-N 2 𝑥 1 2 𝜉 Bessel-J 2 3 2 𝜉 Bessel-Y-Weber 2 3 2 𝜉 {\displaystyle{\displaystyle|x|^{-1/2}{N^{2}}\left(x\right)=\tfrac{1}{2}\xi% \left({J_{2/3}^{2}}\left(\xi\right)+{Y_{2/3}^{2}}\left(\xi\right)\right),}}
    0 references
    DLMF id
    DLMF:9.8.E10
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    Bessel function of the second kind
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2aadec
    0 references
    Airy modulus function
    Defining formula
    N ⁡ ( z ) modulus-Airy-N 𝑧 {\displaystyle{\displaystyle N\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E7.m2acdec
    0 references
    Q11382
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S1.XMD2.m1idec
    0 references
    Q11393
    Defining formula
    ξ 𝜉 {\displaystyle{\displaystyle\xi}}
    xml-id
    C9.S8.XMD1.m1adec
    0 references
     
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