DLMF:8.20.E3 (Q2716)

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DLMF:8.20.E3
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    E p ⁡ ( z ) ∼ ± 2 ⁢ π ⁢ i Γ ⁡ ( p ) ⁢ e ∓ p ⁢ π ⁢ i ⁢ z p - 1 + e - z z ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ ( p ) k z k , asymptotic-expansion exponential-integral-En 𝑝 𝑧 plus-or-minus 2 𝜋 𝑖 Euler-Gamma 𝑝 superscript 𝑒 minus-or-plus 𝑝 𝜋 𝑖 superscript 𝑧 𝑝 1 superscript 𝑒 𝑧 𝑧 superscript subscript 𝑘 0 superscript 1 𝑘 Pochhammer 𝑝 𝑘 superscript 𝑧 𝑘 {\displaystyle{\displaystyle E_{p}\left(z\right)\sim\pm\frac{2\pi i}{\Gamma% \left(p\right)}e^{\mp p\pi i}z^{p-1}+\frac{e^{-z}}{z}\sum_{k=0}^{\infty}\frac{% (-1)^{k}{\left(p\right)_{k}}}{z^{k}},}}
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    DLMF:8.20.E3
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