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The solution of the governing equation representing the drawdown in ahorizontal confined aquifer, where groundwater flow is unsteady, is provided interms of the exponential integral, which is famously known as the Wellfunction. For the computation of this function in practical applications, it isimportant to develop not only accurate but also a simple approximation thatrequires evaluation of the fewest possible terms. To that end, introducingRamanujan's series expression, this work proposes a full-range approximation tothe exponential integral using Ramanujan's series for the small argument (u\leq 1) and an approximation based on the bound of the integral for the otherrange (u \in (1,100]). The evaluation of the proposed approximation results inthe most accurate formulae compared to the existing studies, which possess themaximum percentage error of 0.05\%. Further, the proposed formula is muchsimpler to apply as it contains just the product of exponential and logarithmfunctions. To further check the efficiency of the proposed approximation, weconsider a practical example for evaluating the discrete pumping kernel, whichshows the superiority of this approximation over the others. Finally, theauthors hope that the proposed efficient approximation can be useful forgroundwater and hydrogeological applications.

Full-Range Approximation for the Theis Well Function Using Ramanujan's Series and Bounds for the Exponential Integral