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Formula:2988

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Digital Library of Mathematical Functions ID 6.12.E2

Ei ⁡ ( x ) ∼ e x x ⁢ ( 1 + 1 ! x + 2 ! x 2 + 3 ! x 3 + ⋯ ) , asymptotic-expansion exponential-integral-Ei 𝑥 superscript 𝑒 𝑥 𝑥 1 1 𝑥 2 superscript 𝑥 2 3 superscript 𝑥 3 ⋯ {\displaystyle{\displaystyle\mathrm{Ei}\left(x\right)\sim\frac{e^{x}}{x}\left(% 1+\frac{1!}{x}+\frac{2!}{x^{2}}+\frac{3!}{x^{3}}+\cdots\right),}}


Constraint(s)

x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}} :
  • ! {\displaystyle{\displaystyle!}} :
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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