Approximations for the Hantush M function

A recent paper (Trefry, M.G., 1998. Analytical series expressions for Hanhr sh's M and S functions. Water Resour. Res. 34, 909-913) provided several in teresting results concerning the Hantush M function, an integral that arise s often in analytical solutions for groundwater pumping models. It was demo nstrated that, although an exact result for this integral form is available , there remain significant difficulties in its numerical evaluation. We pro vide some simple approximations to the M function, one of which has a relat ive error of less than 1%, one with a relative error less than 0.1%, and on e with a relative error of less than 0.015%. These approximations are likel y suitable for all practical purposes. (C) 1999 Elsevier Science B.V. All r ights reserved.