DLMF:2.8.E22 (Q957)

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DLMF:2.8.E22
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    Statements

    test
    W n , 1 ⁢ ( u , ξ ) = Ai ⁡ ( u 2 / 3 ⁢ ξ ) ⁢ ∑ s = 0 n - 1 A s ⁢ ( ξ ) u 2 ⁢ s + Ai ′ ⁡ ( u 2 / 3 ⁢ ξ ) ⁢ ∑ s = 0 n - 2 B s ⁢ ( ξ ) u 2 ⁢ s + ( 4 / 3 ) + envAi ⁡ ( u 2 / 3 ⁢ ξ ) ⁢ 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 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 envelope-Airy-Ai superscript 𝑢 2 3 𝜉 Big-O 1 superscript 𝑢 2 𝑛 1 {\displaystyle{\displaystyle W_{n,1}(u,\xi)=\mathrm{Ai}\left(u^{2/3}\xi\right)% \sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}+\mathrm{Ai}'\left(u^{2/3}\xi\right)% \sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+(4/3)}}+\mathrm{envAi}\left(u^{2/3}\xi% \right)O\left(\frac{1}{u^{2n-1}}\right),}}
    0 references
    DLMF id
    DLMF:2.8.E22
    0 references
    Symbols used
    Q10919
    test
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1addec
    0 references
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2addec
    0 references
    Q11082
    test
    envAi ⁡ ( x ) envelope-Airy-Ai 𝑥 {\displaystyle{\displaystyle\mathrm{envAi}\left(\NVar{x}\right)}}
    xml-id
    C2.S8.SS3.p4.m4abdec
    0 references
     
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