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Formula:3419

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Digital Library of Mathematical Functions ID 8.20.E6

E p ⁡ ( λ ⁢ p ) ∼ e - λ ⁢ p ( λ + 1 ) ⁢ p ⁢ ∑ k = 0 ∞ A k ⁢ ( λ ) ( λ + 1 ) 2 ⁢ k ⁢ 1 p k , asymptotic-expansion exponential-integral-En 𝑝 𝜆 𝑝 superscript 𝑒 𝜆 𝑝 𝜆 1 𝑝 superscript subscript 𝑘 0 subscript 𝐴 𝑘 𝜆 superscript 𝜆 1 2 𝑘 1 superscript 𝑝 𝑘 {\displaystyle{\displaystyle E_{p}\left(\lambda p\right)\sim\frac{e^{-\lambda p% }}{(\lambda+1)p}\sum_{k=0}^{\infty}\frac{A_{k}(\lambda)}{(\lambda+1)^{2k}}% \frac{1}{p^{k}},}}


Constraint(s)

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}} : generalized exponential integral
  • p 𝑝 {\displaystyle{\displaystyle p}} : parameter
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • A k ⁢ ( λ ) subscript 𝐴 𝑘 𝜆 {\displaystyle{\displaystyle A_{k}(\lambda)}} : A k ( λ )
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