DLMF:10.21.E41 (Q3348)

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DLMF:10.21.E41
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    Statements

    Defining formula
    j ν , m = ν ⁢ z ⁢ ( ζ ) + z ⁢ ( ζ ) ⁢ ( h ⁢ ( ζ ) ) 2 ⁢ B 0 ⁢ ( ζ ) 2 ⁢ ν + O ⁡ ( 1 ν 3 ) , zero-Bessel-J 𝜈 𝑚 𝜈 𝑧 𝜁 𝑧 𝜁 superscript ℎ 𝜁 2 subscript 𝐵 0 𝜁 2 𝜈 Big-O 1 superscript 𝜈 3 {\displaystyle{\displaystyle j_{\nu,m}=\nu z(\zeta)+\frac{z(\zeta)(h(\zeta))^{% 2}B_{0}(\zeta)}{2\nu}+O\left(\frac{1}{\nu^{3}}\right),}}
    0 references
    DLMF id
    DLMF:10.21.E41
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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
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
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    Q11394
    Defining formula
    a k zero-Airy-Ai 𝑘 {\displaystyle{\displaystyle a_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p1.m5aadec
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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.m11amdec
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    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1pdec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1agdec
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    coefficients (locally)
    Defining formula
    B k ⁢ ( ζ ) subscript 𝐵 𝑘 𝜁 {\displaystyle{\displaystyle B_{k}(\zeta)}}
    xml-id
    C10.S20.XMD5.m1dec
    0 references
    Q11464
    Defining formula
    z ⁢ ( ζ ) 𝑧 𝜁 {\displaystyle{\displaystyle z(\zeta)}}
    xml-id
    C10.S21.XMD7.m1dec
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    function (locally)
    Defining formula
    h ⁢ ( ζ ) ℎ 𝜁 {\displaystyle{\displaystyle h(\zeta)}}
    xml-id
    C10.S21.XMD8.m1dec
    0 references
     
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