DLMF:2.10.E18 (Q1005)

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DLMF:2.10.E18
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    Statements

    Defining formula
    S ⁢ ( α , β , n ) = e i ⁢ n ⁢ β e i ⁢ β - 1 ⁢ n α + O ⁡ ( n α - 1 ) + O ⁡ ( 1 ) , 𝑆 𝛼 𝛽 𝑛 superscript 𝑒 𝑖 𝑛 𝛽 superscript 𝑒 𝑖 𝛽 1 superscript 𝑛 𝛼 Big-O superscript 𝑛 𝛼 1 Big-O 1 {\displaystyle{\displaystyle S(\alpha,\beta,n)=\frac{e^{in\beta}}{e^{i\beta}-1% }n^{\alpha}+O\left(n^{\alpha-1}\right)+O\left(1\right),}}
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    DLMF id
    DLMF:2.10.E18
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    constraint
    n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}
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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.m2addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
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