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中文摘要：
超高阶重力场模型的构制与应用的数值稳定性取决于超高阶次缔合勒让德函数的计算方法。介绍了4种常用的缔合勒让德函数的递推计算方法：标准前向列推法、标准前向行推法、Belikov列推法和跨阶次递推法,并对计算程序做了改进,从计算速度、计算精度两方面分析比较了阶次高至3 060阶的各种方法的优劣。数值试验证明,跨阶次递推法是计算超高阶次缔合勒让德函数较优的方法。
英文摘要：
The numerical stability of the construction and application of the ultra-high degree and order earth＇ s gravity model lies on the computing methods of the ultra-high degree and order normalized associated legendre functions （ALFs）. Four computing methods of ALFs including standard forward column method, standard forward row method, Belikov column method and recursive method between every other order and degree, are discussed and their calculation programs are improvied. Advantages and disadvantages of these methods are analyzed and compared in two aspects： numerical efficiency and numerical accuracy, when the degree and order are up to 3 060. Numerical tests prove that reeursive method between every other order and degree is excellent.
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