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DLMF: §6.9 Continued Fraction ‣ Properties ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals

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6 Exponential, Logarithmic, Sine, and Cosine Integrals Properties 6.8 Inequalities 6.10 Other Series Expansions

§6.9 Continued Fraction

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Keywords:: continued fraction, exponential integrals
Notes:: See Nielsen (1906b, pp. 42–44), or Lorentzen and Waadeland (1992, p. 577).
Permalink:: http://dlmf.nist.gov/6.9
See also:: Annotations for Ch.6

6.9.1		$E_{1}\left(z\right)=\cfrac{e^{-z}}{z+\cfrac{1}{1+\cfrac{1}{z+\cfrac{2}{1+% \cfrac{2}{z+\cfrac{3}{1+\cfrac{3}{z+}}}}}}}\cdots,$
$\|\operatorname{ph}z\|<\pi$ .
ⓘ Symbols: $\pi$ : the ratio of the circumference of a circle to its diameter, $\mathrm{e}$ : base of natural logarithm, $E_{1}\left(\NVar{z}\right)$ : exponential integral, $\operatorname{ph}$ : phase and $z$ : complex variable A&S Ref: 5.1.22 (special case of) Referenced by: §6.18(i) Permalink: http://dlmf.nist.gov/6.9.E1 Encodings: TeX, pMML, png See also: Annotations for §6.9 and Ch.6

See also Cuyt et al. (2008, pp. 287–290).

6.8 Inequalities 6.10 Other Series Expansions

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