# Taylor intervals to calculate inverse Ei(x)

## Description

The Mathematica notebook (extension "nb"), which requires as input the three text files with lists, containing a total of 3909 x 4 numbers, calculates the inverse of the exponential integral Ei[x]. The method and all details are provided in the manuscript "Numerical calculation of the inverse of the exponential integral Ei(x) with a quartic polynomial". The PDF file is the "printed" Mathematica notebook, for inspection of the algorithm without the software. Each entry in the list files with the calculated interval limits consists of four numbers, that represent the exponential integral of the lower limits, the exponential integral of the upper limits, the X0s, and the exponential integral of the X0s; in the case of logarithmic transformation (x >= 10), the natural logarithm of the first two numbers is taken. In the filenames, "Neg" stands for "negative", "Pos" for "positive, and "Eps11" refers to epsilon = 10^-11.

## Files

## Steps to reproduce

See the manuscript "Numerical calculation of the inverse of the exponential integral Ei(x) with a quartic polynomial".