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

§6.9 Continued Fraction

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

6.9.1 $\mathop{E_{1}\/}\nolimits\!\left(z\right)=\cfrac{e^{{-z}}}{z+\cfrac{1}{1+% \cfrac{1}{z+\cfrac{2}{1+\cfrac{2}{z+\cfrac{3}{1+\cfrac{3}{z+}}}}}}}\cdots,$ $|\mathop{\mathrm{ph}\/}\nolimits z|<\pi$ .

Symbols:: : base of exponential function, $\mathop{E_{1}\/}\nolimits\!\left(z\right)$ : exponential integral, $\mathop{\mathrm{ph}\/}\nolimits$ : phase and : 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 Cuyt et al. (2008, pp. 287–290).

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