In this paper, we derive a highly accurate approximation for the probability of detection (PD) of a non-coherent detector operating with Weibull fluctuation targets. To do so, we assume a pulse-to-pulse decorrelation during the coherent processing interval (CPI). Specifically, the proposed approximation is given in terms of: i) a closed-form expression derived in terms of the Fox's H-function, for which we also provide a portable and efficient MATHEMATICA routine; and ii) a fast converging series obtained through a comprehensive calculus of residues. Both solutions are fast and provide very accurate results. In particular, our series representation, besides being a more tractable solution, also exhibits impressive savings in computational load and computation time compared to previous studies. Numerical results and Monte-Carlo simulations corroborated the validity of our expressions.