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

PENG Fu qing 1,YU Jin hai 2 (1.Xi′an Institute of Surveying & Mapping,Xi′an 710054, China; 2.Institute of Surveying and Mapping, Information Engineering University of PLA, Zhengzhou 450052,China)  
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.
【CateGory Index】: P223
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