DLMF:11.11.E17 (Q4083)

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DLMF:11.11.E17
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    Statements

    Defining formula
    𝐀 - Ξ½ ⁑ ( Ξ½ + a ⁒ Ξ½ 1 / 3 ) = 2 1 / 3 ⁒ Ξ½ - 1 / 3 ⁒ Hi ⁑ ( - 2 1 / 3 ⁒ a ) + O ⁑ ( Ξ½ - 1 ) , associated-Anger-Weber-A 𝜈 𝜈 π‘Ž superscript 𝜈 1 3 superscript 2 1 3 superscript 𝜈 1 3 Scorer-Hi superscript 2 1 3 π‘Ž Big-O superscript 𝜈 1 {\displaystyle{\displaystyle\mathbf{A}_{-\nu}\left(\nu+a\nu^{1/3}\right)=2^{1/% 3}\nu^{-1/3}\mathrm{Hi}\left(-2^{1/3}a\right)+O\left(\nu^{-1}\right),}}
    0 references
    DLMF id
    DLMF:11.11.E17
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    Symbols used
    order not exceeding
    Defining formula
    O ⁑ ( x ) Big-O π‘₯ {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
    0 references
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Hi ⁑ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2adec
    0 references
    Anger–Weber function
    Defining formula
    𝐀 Ξ½ ⁑ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E4.m2agdec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1ldec
    0 references
     
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