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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.

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伽玛函数作为水文频率及洪水计算中应用广泛的函数，计算方法众多，适用范围和计算精度各不相同。为探索适合水文计算的高精度伽玛函数计算方法，采用斯特林级数及其衍生的近似式等不同伽玛函数渐进展开公式进行计算分析，比较各种方法的适用范围及计算精度。结果表明，分段多项式法截断误差最小，成果精度最高；其次为Ramanujan渐近展开式和stirling前四项式。推荐的高精度伽玛函数计算方法可提高水文成果的精度，为各类涉水工程规划、设计中确定工程规模和管理决策提供快速精准的成果。

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郭世兴（1973-），男，正高级工程师，研究方向为水文水资源和水利水电工程规划，E-mail：guosx2022@qq.com

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郭世兴（1973-），男，正高级工程师，研究方向为水文水资源和水利水电工程规划，E-mail：guosx2022@qq.com

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