§6.11 Relations to Other Functions

For the notation see §§8.2(i) and 13.2(i).

Incomplete Gamma Function

 6.11.1 $E_{1}\left(z\right)=\Gamma\left(0,z\right).$ ⓘ Symbols: $E_{1}\left(\NVar{z}\right)$: exponential integral, $\Gamma\left(\NVar{a},\NVar{z}\right)$: incomplete gamma function and $z$: complex variable A&S Ref: 5.1.45 (special case of) Referenced by: §6.11 Permalink: http://dlmf.nist.gov/6.11.E1 Encodings: TeX, pMML, png See also: Annotations for §6.11, §6.11 and Ch.6

Confluent Hypergeometric Function

 6.11.2 $E_{1}\left(z\right)=e^{-z}U\left(1,1,z\right),$ ⓘ Symbols: $U\left(\NVar{a},\NVar{b},\NVar{z}\right)$: Kummer confluent hypergeometric function, $\mathrm{e}$: base of natural logarithm, $E_{1}\left(\NVar{z}\right)$: exponential integral and $z$: complex variable Referenced by: §6.11, 5th item, §6.6 Permalink: http://dlmf.nist.gov/6.11.E2 Encodings: TeX, pMML, png See also: Annotations for §6.11, §6.11 and Ch.6
 6.11.3 $\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right)=U\left(1,1,-iz\right).$