ei

The E_n(x) function is defined by the integral E_n(x) congruent integral_1^∞ (e^(-x t) d t)/t^n and is given by the Wolfram Language function ExpIntegralE[n, x]. Defining t congruent η^(-1) so that d t = - η^(-2) d η, E_n(x) = integral_0^1 e^(-x/η) η^(n - 2) d η For integer n>1, E_n(0) = 1/(n - 1). Plots in the complex plane are shown above for E_0(z).

cosine integral | E_t-function | exponential integral | Gompertz constant | sine integral