Approximation for the exponential integral (Theis well function)

In this note, we provide an analytical approximation to the exponential integral valid for all values of its argument. The approximation is constructed by interpolation between the exponential integralʹs small and large asymptotes. The interpolation contains an unknown function, which is determined using the minimax criterion. The maximum error in the approximation is less than 0.07%, making it useful for routine hydrological applications.