Difference between revisions of "Exponential integral E"
From specialfunctionswiki
| Line 22: | Line 22: | ||
=References= | =References= | ||
| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=findme}}: $5.1.1$ | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=findme}}: $5.1.1$ |
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=findme}}: $5.1.4$ | ||
{{:*-integral functions footer}} | {{:*-integral functions footer}} | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 18:34, 7 August 2016
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 $$E_n(z)=\displaystyle\int_1^{\infty} \dfrac{e^{-zt}}{t^n} \mathrm{d}t.$$
Graph of $\mathrm{E}_1$.
Graph of $\mathrm{E}_2$.
Graph of $\mathrm{E}_3$.
Domain coloring of $\mathrm{E}_1$.
Domain coloring of $\mathrm{E}_2$.
Properties
Relationship between the exponential integral and upper incomplete gamma function
Videos
Laplace transform of exponential integral
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $5.1.1$
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $5.1.4$
