As a widely used function in hydrologic frequency and flood computation, the Gamma function has many calculation methods, and the scope of application and computation accuracy also vary. In order to explore a high-precision Gamma function computation method suitable for hydrological computation, different Gamma function asymptotic expansion formulas such as Stirling series and its derived approximation formula are used for computation and analysis. Comparing the accuracy and application range of various methods, the results show that the piecewise polynomial method has the smallest truncation error and the highest accuracy; The second is the Ramanujan asymptotic expansion and the Stirling first tetranomial. The recommendatory high-precision Gamma function computation method can effectively improve the computation accuracy of hydrological results, which can provide fast and accurate results for the planning and design of various hydro projects to determine project scale and management decisions.

hydrological computation  /  Gamma function  /  asymptotic expansion  /  Stirling series