Difference between revisions of "Exponential integral E"
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(Created page with "The exponential integrals are $$\mathrm{Ei}(x) = \int_{-\infty}^x \dfrac{e^t}{t} dt$$ and $$E_1(x) = \int_x^{\infty} \dfrac{e^{-t}}{t} dt.$$ Simple properties of integrals imp...") |
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$$E_1(x) = \int_x^{\infty} \dfrac{e^{-t}}{t} dt.$$ | $$E_1(x) = \int_x^{\infty} \dfrac{e^{-t}}{t} dt.$$ | ||
| − | Simple properties of integrals imply that $E_1(x) = -\mathrm{Ei}(-x)$. | + | Simple properties of integrals imply that $E_1(x) = -\mathrm{Ei}(-x)$. The exponential integral is related to the [[logarithmic integral]] by the formula |
| + | $$\mathrm{li}(x)=\mathrm{Ei}( \log(x)).$$ | ||
Revision as of 20:58, 4 October 2014
The exponential integrals are $$\mathrm{Ei}(x) = \int_{-\infty}^x \dfrac{e^t}{t} dt$$ and $$E_1(x) = \int_x^{\infty} \dfrac{e^{-t}}{t} dt.$$ Simple properties of integrals imply that $E_1(x) = -\mathrm{Ei}(-x)$. The exponential integral is related to the logarithmic integral by the formula $$\mathrm{li}(x)=\mathrm{Ei}( \log(x)).$$
