Calculation of the generalized leaky aquifer integral

We provide a convenient method for the evaluation of the generalized leaky aquifer integral Wβ(x,y), for all real x,y>0 and integers and half odd integers β⩾12. The key ingredient to obtaining values for higher β is a new asymptotic expansion of the integral that is applicable for a wide range of these parameters, particularly large β. An asymptotic value and a value, calculated via previously published methods, for the same x and y but small β, form a well defined two-point boundary value problem that is easily solved.