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超过2 000阶次的缔合勒让德函数值的递推计算,在接近两极时达到极大的数量级(超过10的数千次方),这导致现有递推方法在计算缔合勒让德函数值及其导数值时失效。通过插入压缩因子技术,提出一个修改的递推算法,并结合使用Horner求和技术计算球谐级数的部分和。试验表明,该算法至少可以计算到3 600完全阶次的球谐级数式,优于现有结果。 更多还原

【Abstract】 When evaluated increasingly close to the poles,the computations of the very high degree and order(e.g.over 2 000) associated Legendre functions exhibit extremely large ranges(over thousands of orders) of magnitudes.This causes existing recursion techniques for computing values of associated Legendre functions and their derivatives to fail.A modified recursion algorithm is proposed for computing associated Legendre functions and their first derivatives by a scale factor.The modified recursions yi... 更多还原