DLMF:2.11.E15 (Q1040)

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DLMF:2.11.E15
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    Defining formula
    F n + p ⁡ ( z ) ∼ ( - 1 ) n ⁢ i ⁢ e - p ⁢ π ⁢ i ⁢ ( 1 2 ⁢ erfc ⁡ ( 1 2 ⁢ ρ ⁢ c ⁢ ( θ ) ) - i ⁢ e i ⁢ ρ ⁢ ( π - θ ) ⁢ e - ρ - z ( 2 ⁢ π ⁢ ρ ) 1 / 2 ⁢ ∑ s = 0 ∞ h 2 ⁢ s ⁢ ( θ , α ) ρ s ) . asymptotic-expansion terminant-function 𝑛 𝑝 𝑧 superscript 1 𝑛 𝑖 superscript 𝑒 𝑝 𝜋 𝑖 1 2 complementary-error-function 1 2 𝜌 𝑐 𝜃 𝑖 superscript 𝑒 𝑖 𝜌 𝜋 𝜃 superscript 𝑒 𝜌 𝑧 superscript 2 𝜋 𝜌 1 2 superscript subscript 𝑠 0 subscript ℎ 2 𝑠 𝜃 𝛼 superscript 𝜌 𝑠 {\displaystyle{\displaystyle F_{n+p}\left(z\right)\sim(-1)^{n}ie^{-p\pi i}% \left(\tfrac{1}{2}\operatorname{erfc}\left(\sqrt{\tfrac{1}{2}\rho}\,c(\theta)% \right)-i\frac{e^{i\rho(\pi-\theta)}e^{-\rho-z}}{(2\pi\rho)^{1/2}}\sum_{s=0}^{% \infty}\frac{h_{2s}(\theta,\alpha)}{\rho^{s}}\right).}}
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    DLMF id
    DLMF:2.11.E15
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