eiE0

eiE0 is a term encountered in scattered mathematical and scientific contexts, but it does not correspond to a single standardized object. In many cases it is used as a symbolic label for a quantity evaluated at a reference energy E0, or, in a mathematical setting, as shorthand for the exponential integral function Ei evaluated at the argument E0 (that is, Ei(E0)).

In mathematics, Ei(x) denotes the exponential integral, defined by Ei(x) = γ + ln|x| + ∑_{n=1}^∞ x^n/(n·n!) for x near 0, where γ is the Euler–Mascheroni constant. The function has a logarithmic singularity at x = 0, so Ei(0) is undefined. For small positive or negative E0, Ei(E0) behaves as γ + ln|E0| plus higher-order terms. When used as Ei(E0), the value of eiE0 depends on the specific numerical value and sign of E0.

In physics or engineering usages, E0 commonly denotes a reference, threshold, or initial energy. In such contexts eiE0 may refer to a quantity defined by integrating or evaluating a model at the energy E0, rather than to the Ei function itself. Definitions and interpretations are therefore varyingly contingent on the source and application.

Because eiE0 is not a universally standardized term, readers should consult the original source for the precise definition and notation. See also Exponential integral, Ei, and E0.