| 缔合勒让德函数的标准向前按列递推公式 |
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| 引用本文： | 张捍卫,张华,李鹏杰.缔合勒让德函数的标准向前按列递推公式[J].大地测量与地球动力学,2022,42(2):111-114. |
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| 作者姓名： | 张捍卫 张华 李鹏杰 |
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| 作者单位： | 河南理工大学测绘与国土信息工程学院,河南省焦作市世纪大道2001号,454000 |
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| 基金项目： | 国家自然科学基金(42074002,41931075)。 |
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| 摘 要： | 针对推导扇谐项（次等于阶的项）和准扇谐项（次等于阶减1的项）存在不严谨性的问题，给出基于fnALFs的2个导数定积分按列递推公式，结果与已有的研究结论完全一致，但推导过程更简明，且该定积分公式可从第2阶开始递推。另外，本文还给出另外2个fnALFs定积分计算公式。
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| 关 键 词： | 缔合勒让德函数 完全规格化缔合勒让德函数 fnALFs定积分 标准向前按列递推公式 |
The Standard Forward Column Recurrence Formula of ALFs |
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| ZHANG Hanwei,ZHANG Hua,LI Pengjie.The Standard Forward Column Recurrence Formula of ALFs[J].Journal of Geodesy and Geodynamics,2022,42(2):111-114. |
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| Authors: | ZHANG Hanwei ZHANG Hua LI Pengjie |
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| Institution: | (School of Surveying and Land Information Engineering,Henan Polytechnic University,2001 Shiji Road,Jiaozuo 454000,China) |
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| Abstract: | There are some inaccuracies in the derivation of the sectorial harmonic term (order is equal to degree) and the quasi-sectorial harmonic term (order is equal to degree minus 1) in the related literature, and we give a strict derivation method. Based on the two derivative formulas of fnALFs, we give the standard forward column recurrence formula of its definite integration; the results are completely consistent with those given by predecessors, but the derivation process is more concise, which can be recursed from the second degree. In addition, we derive two other useful definite integration formulas of fnALFs. |
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| Keywords: | associated Legendre functions fully normalized associated Legendre functions the definite integral for fnALFs standard forward column recurrence formula |
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