DLMF:2.8.E15 (Q949)

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DLMF:2.8.E15
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    Statements

    Defining formula
    W n , 1 ⁢ ( u , ξ ) = Ai ⁡ ( u 2 / 3 ⁢ ξ ) ⁢ ( ∑ s = 0 n - 1 A s ⁢ ( ξ ) u 2 ⁢ s + O ⁡ ( 1 u 2 ⁢ n - 1 ) ) + Ai ′ ⁡ ( u 2 / 3 ⁢ ξ ) ⁢ ( ∑ s = 0 n - 2 B s ⁢ ( ξ ) u 2 ⁢ s + ( 4 / 3 ) + O ⁡ ( 1 u 2 ⁢ n - 1 ) ) , subscript 𝑊 𝑛 1 𝑢 𝜉 Airy-Ai superscript 𝑢 2 3 𝜉 superscript subscript 𝑠 0 𝑛 1 subscript 𝐴 𝑠 𝜉 superscript 𝑢 2 𝑠 Big-O 1 superscript 𝑢 2 𝑛 1 diffop Airy-Ai 1 superscript 𝑢 2 3 𝜉 superscript subscript 𝑠 0 𝑛 2 subscript 𝐵 𝑠 𝜉 superscript 𝑢 2 𝑠 4 3 Big-O 1 superscript 𝑢 2 𝑛 1 {\displaystyle{\displaystyle W_{n,1}(u,\xi)=\mathrm{Ai}\left(u^{2/3}\xi\right)% \left(\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}+O\left(\frac{1}{u^{2n-1}}% \right)\right)+\mathrm{Ai}'\left(u^{2/3}\xi\right)\left(\sum_{s=0}^{n-2}\frac{% B_{s}(\xi)}{u^{2s+(4/3)}}+O\left(\frac{1}{u^{2n-1}}\right)\right),}}
    0 references
    DLMF id
    DLMF:2.8.E15
    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.m1adec
    0 references
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2abdec
    0 references
    Q11077
    Defining formula
    W n , j ⁢ ( u , ξ ) subscript 𝑊 𝑛 𝑗 𝑢 𝜉 {\displaystyle{\displaystyle W_{n,j}(u,\xi)}}
    xml-id
    C2.S8.XMD15.m1adec
    0 references
    Q11078
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S8.XMD16.m1dec
    0 references
    Q11079
    Defining formula
    A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    xml-id
    C2.S8.XMD17.m1dec
    0 references
    Q11080
    Defining formula
    B s ⁢ ( ξ ) subscript 𝐵 𝑠 𝜉 {\displaystyle{\displaystyle B_{s}(\xi)}}
    xml-id
    C2.S8.XMD18.m1dec
    0 references
    Q11069
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C2.S8.XMD4.m1hdec
    0 references
     
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