Expint

expint(n,z) returns the exponential integral of order n, where n is an integer >= 0. This is the integral from 1 to infinity of t^(-n) e^(-tz) dt.

If your copy of gnuplot was built with support for complex functions from the Amos library, then for n>0 the evaluation uses Amos routine cexint [Amos 1990 Algorithm 683, ACM Trans Math Software 16:178]. In this case z may be any complex number with -pi < arg(z) <= pi. expint(0,z) is calculated as exp(-z)/z.

If Amos library support is not present, z is limited to real values z >= 0.