Exponential integral E

From specialfunctionswiki
Revision as of 00:22, 19 June 2016 by Tom (talk | contribs)
Jump to: navigation, search

The exponential integral functions $E_n$ are defined for $\left|\mathrm{arg \hspace{2pt}}z\right|<\pi$ by $$E_1(z) = \displaystyle\int_1^{\infty} \dfrac{e^{-t}}{t} \mathrm{d}t,$$ and $$E_n(z)=\displaystyle\int_1^{\infty} \dfrac{e^{-zt}}{t^n} \mathrm{d}t.$$

Properties

Relationship between the exponential integral and upper incomplete gamma function

Videos

Laplace transform of exponential integral

References

Exponential Integral and Related Functions

$\ast$-integral functions