张捍卫,杨永勤,张华,李晓玲

• 1:河南理工大学测绘与国土信息工程学院

摘要(Abstract)：

缔合勒让德函数是地球科学领域中的主要数学工具之一。针对超高阶球谐重力场模型的构建与快速计算，以及跨阶次递推公式的适用性问题，该文利用勒让德函数的原理性公式，给出了3种类型的跨阶次递推公式。当次为0和1时，第1种采用了标准向前按列递推公式，第2和第3种则是采用了列式递推公式。其中，第一种是学界经常采用的公式。研究表明，在要求相对误差为1.0E-11情况下，3种类型的跨阶次递推公式都可以至少递推至15 000阶。在两个极点处，第2种和第3种算法的适用性优于第1种算法，但是第1种算法的计算精度优于后两种算法。

关键词(KeyWords)： 缔合勒让德函数(ALFs);完全规格化的缔合勒让德函数(fnALFs);跨阶次递推公式;适用性和普适性

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(42074002,41931075)

作者(Author): 张捍卫,杨永勤,张华,李晓玲

DOI: 10.16251/j.cnki.1009-2307.2022.09.006

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