DLMF:2.9.E9 (Q982)

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DLMF:2.9.E9
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    Statements

    Defining formula
    w j ⁢ ( n ) ∼ ρ n ⁢ exp ⁡ ( ( - 1 ) j ⁢ κ ⁢ n ) ⁢ n α ⁢ ∑ s = 0 ∞ ( - 1 ) j ⁢ s ⁢ c s n s / 2 , asymptotic-expansion subscript 𝑤 𝑗 𝑛 superscript 𝜌 𝑛 superscript 1 𝑗 𝜅 𝑛 superscript 𝑛 𝛼 superscript subscript 𝑠 0 superscript 1 𝑗 𝑠 subscript 𝑐 𝑠 superscript 𝑛 𝑠 2 {\displaystyle{\displaystyle w_{j}(n)\sim\rho^{n}\exp\left((-1)^{j}\kappa\sqrt% {n}\right)n^{\alpha}\sum_{s=0}^{\infty}(-1)^{js}\frac{c_{s}}{n^{s/2}},}}
    0 references
    DLMF id
    DLMF:2.9.E9
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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    Q11103
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C2.S9.XMD10.m1dec
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    Q11104
    Defining formula
    κ 𝜅 {\displaystyle{\displaystyle\kappa}}
    xml-id
    C2.S9.XMD11.m1dec
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    Q11105
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C2.S9.XMD14.m1dec
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    Q11102
    Defining formula
    w j ⁢ ( n ) subscript 𝑤 𝑗 𝑛 {\displaystyle{\displaystyle w_{j}(n)}}
    xml-id
    C2.S9.XMD9.m1adec
    0 references
     
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