Hantush Well Function revisited

In this paper, we comment on some recent numerical and analytical work to evaluate the Hantush Well Function. We correct an expression found in a Comment by Nadarajah [Nadarajah, S., 2007. A comment on numerical evaluation of Theis and Hantush–Jacob well functions. Journal of Hydrology 338, 152–153] to a paper by Prodanoff et al. [Prodanoff, J.A., Mansur, W.J., Mascarenhas, F.C.B., 2006. Numerical evaluation of Theis and Hantush–Jacob well functions. Journal of Hydrology 318, 173–183]. We subsequently derived another analytic representation based on a generalized hypergeometric function in two variables and from the hydrological literature we cite an analytic representation by Hunt [Hunt, B., 1977. Calculation of the leaky aquifer function. Journal of Hydrology 33, 179–183]. We have implemented both representations and compared the results. Using a convergence accelerator Hunt’s representation of Hantush Well Function is efficient and accurate. While checking our implementations we found that Bear’s table of the Hantush Well Function [Bear, J., 1979. Hydraulics of Groundwater. McGraw-Hill, New York, Tables 8–6] contains a number of typographical errors that are not present in the original table published by Hantush [Hantush, M.S., 1956. Analysis of data from pumping tests in leaky aquifers. Transactions, American Geophysical Union 37, 702–714]. Finally, we offer a very fast approximation with a maximum relative error of 0.0033 for the parameter range in the table given by Bear.