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Formula:3395

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Digital Library of Mathematical Functions ID 8.19.E11

E p ⁡ ( z ) = Γ ⁡ ( 1 - p ) ⁢ ( z p - 1 - e - z ⁢ ∑ k = 0 ∞ z k Γ ⁡ ( 2 - p + k ) ) , exponential-integral-En 𝑝 𝑧 Euler-Gamma 1 𝑝 superscript 𝑧 𝑝 1 superscript 𝑒 𝑧 superscript subscript 𝑘 0 superscript 𝑧 𝑘 Euler-Gamma 2 𝑝 𝑘 {\displaystyle{\displaystyle E_{p}\left(z\right)=\Gamma\left(1-p\right)\left(z% ^{p-1}-e^{-z}\sum_{k=0}^{\infty}\frac{z^{k}}{\Gamma\left(2-p+k\right)}\right),}}


Constraint(s)

Symbols List

  • Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}} : gamma function
  • 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
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • p 𝑝 {\displaystyle{\displaystyle p}} : parameter
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  •  Edit this on Wikidata

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