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DLMF: §6.8 Inequalities ‣ Properties ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals

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6 Exponential, Logarithmic, Sine, and Cosine Integrals Properties 6.7 Integral Representations 6.9 Continued Fraction

§6.8 Inequalities

ⓘ

Keywords:: exponential integrals, inequalities
Notes:: See Gautschi (1959b) for (6.8.1), and Luke (1969b, p. 201) for (6.8.2) and (6.8.3).
Permalink:: http://dlmf.nist.gov/6.8
See also:: Annotations for Ch.6

In this section $x>0$ .

6.8.1		$\frac{1}{2}\ln\left(1+\frac{2}{x}\right)<e^{x}E_{1}\left(x\right)<\ln\left(1+% \frac{1}{x}\right),$
ⓘ Symbols: $\mathrm{e}$ : base of natural logarithm, $E_{1}\left(\NVar{z}\right)$ : exponential integral, $\ln\NVar{z}$ : principal branch of logarithm function and $x$ : real variable A&S Ref: 5.1.20 Referenced by: §6.8 Permalink: http://dlmf.nist.gov/6.8.E1 Encodings: TeX, pMML, png See also: Annotations for §6.8 and Ch.6

6.8.2		$\frac{x}{x+1}<xe^{x}E_{1}\left(x\right)<\frac{x+1}{x+2},$
ⓘ Symbols: $\mathrm{e}$ : base of natural logarithm, $E_{1}\left(\NVar{z}\right)$ : exponential integral and $x$ : real variable Referenced by: §6.8 Permalink: http://dlmf.nist.gov/6.8.E2 Encodings: TeX, pMML, png See also: Annotations for §6.8 and Ch.6

6.8.3		$\frac{x(x+3)}{x^{2}+4x+2}<xe^{x}E_{1}\left(x\right)<\frac{x^{2}+5x+2}{x^{2}+6x% +6}.$
ⓘ Symbols: $\mathrm{e}$ : base of natural logarithm, $E_{1}\left(\NVar{z}\right)$ : exponential integral and $x$ : real variable Referenced by: §6.8 Permalink: http://dlmf.nist.gov/6.8.E3 Encodings: TeX, pMML, png See also: Annotations for §6.8 and Ch.6

6.7 Integral Representations 6.9 Continued Fraction

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