 Exponential integral

For real $x>0$, the decaying exponential integral isThe other standard real convention satisfies $\mathrm{Ei}(-x)=-E_1(x)$. The NIST definitions specify the analytic continuation and branch conventions.

The Exponential Integral, commonly denoted as \( \text{Ei}(x) \), is a special function that arises frequently in mathematics, specifically in the context of integral calculus, complex analysis, and applied mathematics.