Difference between revisions of "Exponential integral E"
From specialfunctionswiki
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[https://www.youtube.com/watch?v=TppV_yDY3EQ Laplace transform of exponential integral]<br /> | [https://www.youtube.com/watch?v=TppV_yDY3EQ Laplace transform of exponential integral]<br /> | ||
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| + | [[Exponential integral Ei]] | ||
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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
See Also
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): $5.1.4$
