DLMF:2.8.E12 (Q946)

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DLMF:2.8.E12
No description defined

    Statements

    Defining formula
    W n , 2 ⁢ ( u , ξ ) = e - u ⁢ ξ ⁢ ( ∑ s = 0 n - 1 ( - 1 ) s ⁢ A s ⁢ ( ξ ) u s + O ⁡ ( 1 u n ) ) , subscript 𝑊 𝑛 2 𝑢 𝜉 superscript 𝑒 𝑢 𝜉 superscript subscript 𝑠 0 𝑛 1 superscript 1 𝑠 subscript 𝐴 𝑠 𝜉 superscript 𝑢 𝑠 Big-O 1 superscript 𝑢 𝑛 {\displaystyle{\displaystyle W_{n,2}(u,\xi)=e^{-u\xi}\left(\sum_{s=0}^{n-1}(-1% )^{s}\frac{A_{s}(\xi)}{u^{s}}+O\left(\frac{1}{u^{n}}\right)\right),}}
    0 references
    DLMF id
    DLMF:2.8.E12
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    constraint
    ξ ∈ 𝚫 2 ⁢ ( α 2 ) 𝜉 subscript 𝚫 2 subscript 𝛼 2 {\displaystyle{\displaystyle\xi\in\mathbf{\Delta}_{2}(\alpha_{2})}}
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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.m2aadec
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    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    Q11074
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S8.XMD10.m1adec
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    Q11073
    Defining formula
    W n , j ⁢ ( u , ξ ) subscript 𝑊 𝑛 𝑗 𝑢 𝜉 {\displaystyle{\displaystyle W_{n,j}(u,\xi)}}
    xml-id
    C2.S8.XMD11.m1bdec
    0 references
    Q11075
    Defining formula
    A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    xml-id
    C2.S8.XMD12.m1adec
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    Q11076
    Defining formula
    𝚫 j ⁢ ( α j ) subscript 𝚫 𝑗 subscript 𝛼 𝑗 {\displaystyle{\displaystyle\mathbf{\Delta}_{j}(\alpha_{j})}}
    xml-id
    C2.S8.XMD13.m1adec
    0 references
    Q11069
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C2.S8.XMD4.m1fdec
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