一类球谐函数与三角函数乘积积分的计算

The computation on a sort of integrals of the product of spherical harmonics and trigonometric functions

本文根据球谐函数的跨次递推公式和三角函数的性质,详细推导了在重力梯度调和分析中出现的一类球谐函数积分的跨次递推公式和递推初始值的计算公式。数值试验表明,球谐函数跨次递推算法具有快速、稳定的优点。该类积分的跨次递推实现,为卫星重力梯度调和分析奠定了算法基础。

In this paper, a sort of recursive formulas of spherical harmonics integrals, which often appear in the gravitational gradient harmonic analysis, are deduced according to the recursive formulas between every other order of spherical harmonics and the trigonometric functions' properties. And the calculated formulas on the recursive initialization also are brought forward. The recursive formulas of the spherical harmonics integral between every other order are proved to be fast and stable by numerical computation. The numerical realization of the sort of integrals establishes algorithmic foundation of the satellite gravitational gradient harmonic analysis.