Approximations for the Hantush M function

Andrew Barry, J.-Y Parlange, Martin Crapper

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


A recent paper (Trefry, M.G., 1998. Analytical series expressions for Hantush's M and S functions. Water Resour. Res. 34, 909–913) provided several interesting results concerning the Hantush M function, an integral that arises often in analytical solutions for groundwater pumping models. It was demonstrated that, although an exact result for this integral form is available, there remain significant difficulties in its numerical evaluation. We provide some simple approximations to the M function, one of which has a relative error of less than 1%, one with a relative error less than 0.1%, and one with a relative error of less than 0.015%. These approximations are likely suitable for all practical purposes.
Original languageEnglish
Pages (from-to)91-96
JournalJournal of Hydrology
Issue number1-2
Early online date4 Aug 1999
Publication statusPublished - 16 Aug 1999


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