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Formula:2971

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Digital Library of Mathematical Functions ID 6.9.E1

E 1 ⁡ ( z ) = e - z z + 1 1 + 1 z + 2 1 + 2 z + 3 1 + 3 z + ⁢ ⋯ , exponential-integral 𝑧 continued-fraction superscript 𝑒 𝑧 𝑧 continued-fraction 1 1 continued-fraction 1 𝑧 continued-fraction 2 1 continued-fraction 2 𝑧 continued-fraction 3 1 continued-fraction 3 limit-from 𝑧 ⋯ {\displaystyle{\displaystyle E_{1}\left(z\right)=\cfrac{e^{-z}}{z+\cfrac{1}{1+% \cfrac{1}{z+\cfrac{2}{1+\cfrac{2}{z+\cfrac{3}{1+\cfrac{3}{z+}}}}}}}\cdots,}}


Constraint(s)

| ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}

Symbols List

  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}} : exponential integral
  • ph phase {\displaystyle{\displaystyle\operatorname{ph}}} : phase
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  •  Edit this on Wikidata

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