DLMF:9.6.E12 (Q2792)

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DLMF:9.6.E12
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    Statements

    Defining formula
    J ± 2 / 3 ⁡ ( ζ ) = 1 2 ⁢ ( 3 / z ) ⁢ ( ± 3 ⁢ Ai ′ ⁡ ( - z ) + Bi ′ ⁡ ( - z ) ) , Bessel-J plus-or-minus 2 3 𝜁 1 2 3 𝑧 plus-or-minus 3 diffop Airy-Ai 1 𝑧 diffop Airy-Bi 1 𝑧 {\displaystyle{\displaystyle J_{\pm 2/3}\left(\zeta\right)=\tfrac{1}{2}(\sqrt{% 3}/z)\left(\pm\sqrt{3}\mathrm{Ai}'\left(-z\right)+\mathrm{Bi}'\left(-z\right)% \right),}}
    0 references
    DLMF id
    DLMF:9.6.E12
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1aedec
    0 references
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2aedec
    0 references
    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.m2aedec
    0 references
    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1kdec
    0 references
    change of variable (locally)
    Defining formula
    ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}}
    xml-id
    C9.S6.XMD2.m1bdec
    0 references
     
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