The exponential integrals \(E_1(x)\), \(E_2(x)\), \(E_n(x)\) and \(Ei(x)\), and the incomplete gamma function \(\Gamma(a, x)\) that is defined for negative values of its first argument.
The exponential integral $$ E_1(x) = \int_x^\infty \frac{e^{-t}}{t}\, dt$$ and the incomplete gamma function $$ \Gamma(a, x) = \int_x^\infty t^{a-1} e^{-t}\, dt$$ are closely related functions that arise in various fields of mathematics.
expint is a small package that provides R functions to compute the exponential integral and the incomplete gamma function.
Most conveniently for R package developers, the package also gives access to the underlying C workhorses through an API; see the package vignette for instructions.
The C routines are adapted versions of those of the GNU Scientific Library https://www.gnu.org/software/gsl/.
Abramowitz, M. and Stegun, I. A. (1972), Handbook of Mathematical Functions, Dover.
expint for the exponential integral family of functions.
gammainc for the incomplete gamma function.
vignette("expint") for a detailed presentation of the package.