  It is pointed out that Hantush's \emph{M} function, commonly used in
groundwater pumping modeling, is identical to the function known in the
problems of heat conduction in the ground. A modified Hantush function $E$ used
in the steady-state solutions for heat conduction that take into account
advection due to groundwater flow around borehole heat exchangers (BHEs) is
introduced. New exact representation and two-types of approximate expressions
for this two-parametric function \emph{E} are presented: one is suitable for
small values of a parameter and the other for its large values. High accuracy
of the approximate formulae is verified by comparison with the exact values
provided by modified Hantush's function $E$ in those validity domains. These
analytical expressions can be used for designing complex borehole
configurations and may be potentially useful in steady-state analysis of
partially penetrated wells (PPWs) in leaky aquifer.
