DLMF:8.11.E18 (Q2591)

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DLMF:8.11.E18
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    Statements

    test
    S n ⁢ ( x ) ∼ ∑ k = 0 ∞ d k ⁢ ( x ) ⁢ n - k , asymptotic-expansion subscript 𝑆 𝑛 𝑥 superscript subscript 𝑘 0 subscript 𝑑 𝑘 𝑥 superscript 𝑛 𝑘 {\displaystyle{\displaystyle S_{n}(x)\sim\sum_{k=0}^{\infty}d_{k}(x)n^{-k},}}
    0 references
    DLMF id
    DLMF:8.11.E18
    0 references
    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
    0 references
    Symbols used
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aedec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1gdec
    0 references
    Q11330
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1fdec
    0 references
    Q11329
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1gdec
    0 references
    function (locally)
    test
    S n ⁢ ( x ) subscript 𝑆 𝑛 𝑥 {\displaystyle{\displaystyle S_{n}(x)}}
    xml-id
    C8.S11.XMD6.m1ddec
    0 references
    Q11347
    test
    d k ⁢ ( x ) subscript 𝑑 𝑘 𝑥 {\displaystyle{\displaystyle d_{k}(x)}}
    xml-id
    C8.S11.XMD7.m1dec
    0 references
     
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