球冠谐分析中非整阶Legendre函数的性质及其计算

局部重力场的谱方法是当前重力学的研究方向，该方法的核心问题是如何构造合适的谱函数以及如何对谱函数实施快速、有效的计算。当所研究的区域近似一个球冠时，迂冠谐函数是该区域对应的谱函数，它由非整阶勒让德（Ｌｅｇｅｎｄｒｅ）函数和三角函数组成，显然非整阶勒让德函数的构造和计算是研究球冠谐函数的关键。本文研究了非高小阶勒让德函数的性质和实用计算方法，包括如何对非整阶勒让德函数实施规格化处理。

The Characters and Computation of Legendre Function with Non-integral Degree in SCHA

In contemporary Earth sciences it is an alternative approach to local gravity field representation by spectral method, which faces a crucial problem that is how to construct and compute perfect spectral functions. The SCH function, which comprises trigonometric functions and associated Legendre function with integral order but non integral degree, is the kind of spectral function if the shape of the local field is near to a spherical cap.Evidently,it is a key how to construct and compute the Legendre function with non integral degree.In this paper,we have studied the theory of constructing and computing the Legendre function with nonintegral degree, including how to normalize it.