Difference between revisions of "Exponential integral E"
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| − | The exponential integral functions $E_n$ are defined for $\left|\mathrm{arg \hspace{2pt}}z\right|<\pi$ by | + | The exponential integral functions $E_n$ are defined for $\left|\mathrm{arg \hspace{2pt}}z\right|<\pi$ and $n=1,2,3,\ldots$ by |
$$E_1(z) = \displaystyle\int_1^{\infty} \dfrac{e^{-t}}{t} \mathrm{d}t,$$ | $$E_1(z) = \displaystyle\int_1^{\infty} \dfrac{e^{-t}}{t} \mathrm{d}t,$$ | ||
and | and | ||
Revision as of 23:59, 10 December 2016
The exponential integral functions $E_n$ are defined for $\left|\mathrm{arg \hspace{2pt}}z\right|<\pi$ and $n=1,2,3,\ldots$ 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
Symmetry relation of exponential integral E
Recurrence relation of exponential integral E
Videos
Laplace transform of exponential integral (2 January 2015)
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): $5.1.4$
