Approximation for the exponential integral (Theis well function)

By D. Barry, J. Parlange, Ling Li. 2000

66 citations recorded by the source corpus.

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 integral's 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.

Subfields: Environmental Engineering, Mechanical Engineering, Oceanography

View Paper: https://www.semanticscholar.org/paper/d1359a5f96e543c18dc204bfec16ed1e417cbb44