DLMF:10.21.E44 (Q3351)

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DLMF:10.21.E44
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    Statements

    Defining formula
    J ν ⁡ ( j ν , m ′ ) = h ⁢ ( ζ ) ⁢ Ai ⁡ ( a m ′ ) ν 1 3 ⁢ ( 1 + O ⁡ ( 1 ν 4 3 ) ) , Bessel-J 𝜈 diffop zero-Bessel-J 𝜈 𝑚 1 ℎ 𝜁 Airy-Ai zero-derivative-Airy-Ai 𝑚 superscript 𝜈 1 3 1 Big-O 1 superscript 𝜈 4 3 {\displaystyle{\displaystyle J_{\nu}\left(j_{\nu,m}'\right)=\frac{h(\zeta)% \mathrm{Ai}\left(a^{\prime}_{m}\right)}{\nu^{\frac{1}{3}}}\left(1+O\left(\frac% {1}{\nu^{\frac{4}{3}}}\right)\right),}}
    0 references
    DLMF id
    DLMF:10.21.E44
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    constraint
    ζ = ν - 2 3 ⁢ a m ′ 𝜁 superscript 𝜈 2 3 zero-derivative-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a^{\prime}_{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.m1aadec
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    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.m2agdec
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    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2acdec
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    Q11456
    Defining formula
    j ν , m zero-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}
    xml-id
    C10.S21.SS1.p2.m11apdec
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    Q11395
    Defining formula
    a k ′ zero-derivative-Airy-Ai 𝑘 {\displaystyle{\displaystyle a^{\prime}_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p1.m11abdec
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    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1sdec
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