Exponential integral E
From specialfunctionswiki
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 $$\mathrm{li}(x)=\mathrm{Ei}( \log(x)).$$
