DLMF:10.21.E42 (Q3349)

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DLMF:10.21.E42
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    Statements

    Defining formula
    J ν ′ ⁡ ( j ν , m ) = - 2 ν 2 3 ⁢ Ai ′ ⁡ ( a m ) z ⁢ ( ζ ) ⁢ h ⁢ ( ζ ) ⁢ ( 1 + O ⁡ ( 1 ν 2 ) ) , diffop Bessel-J 𝜈 1 zero-Bessel-J 𝜈 𝑚 2 superscript 𝜈 2 3 diffop Airy-Ai 1 zero-Airy-Ai 𝑚 𝑧 𝜁 ℎ 𝜁 1 Big-O 1 superscript 𝜈 2 {\displaystyle{\displaystyle J_{\nu}'\left(j_{\nu,m}\right)=-\frac{2}{\nu^{% \frac{2}{3}}}\frac{\mathrm{Ai}'\left(a_{m}\right)}{z(\zeta)h(\zeta)}\left(1+O% \left(\frac{1}{\nu^{2}}\right)\right),}}
    0 references
    DLMF id
    DLMF:10.21.E42
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    constraint
    ζ = ν - 2 3 ⁢ a m 𝜁 superscript 𝜈 2 3 zero-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a_{m}}}
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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
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