DLMF:2.11.E13 (Q1038)

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DLMF:2.11.E13
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    Statements

    test
    F n + p ⁡ ( z ) ∼ e - i ⁢ ( ρ + α ) ⁢ θ 1 + e - i ⁢ θ ⁢ e - ρ - z ( 2 ⁢ π ⁢ ρ ) 1 / 2 ⁢ ∑ s = 0 ∞ a 2 ⁢ s ⁢ ( θ , α ) ρ s , asymptotic-expansion terminant-function 𝑛 𝑝 𝑧 superscript 𝑒 𝑖 𝜌 𝛼 𝜃 1 superscript 𝑒 𝑖 𝜃 superscript 𝑒 𝜌 𝑧 superscript 2 𝜋 𝜌 1 2 superscript subscript 𝑠 0 subscript 𝑎 2 𝑠 𝜃 𝛼 superscript 𝜌 𝑠 {\displaystyle{\displaystyle F_{n+p}\left(z\right)\sim\frac{e^{-i(\rho+\alpha)% \theta}}{1+e^{-i\theta}}\frac{e^{-\rho-z}}{(2\pi\rho)^{1/2}}\sum_{s=0}^{\infty% }\frac{a_{2s}(\theta,\alpha)}{\rho^{s}},}}
    0 references
    DLMF id
    DLMF:2.11.E13
    0 references
    constraint
    ρ → ∞ → 𝜌 {\displaystyle{\displaystyle\rho\to\infty}}
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    Symbols used
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
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