Paper Title:
The Analysis of the Associated Legendre Functions with Non-Integral Degree
  Abstract

Spherical cap harmonic (SCH) theory has been widely used to format regional model of fields that can be expressed as the gradient of a scalar potential. The functions of this method consist of trigonometric functions and associated Legendre functions with integral-order but non-integral degree. Evidently, the constructing and computing of Legendre functions are the core content of the spherical cap functions. In this paper,the approximated calculation method of the normalized association Legendre functions with non-integral degree is introduced and an analysis of the entire order of associated non-Legendre function calculation is presented. Besides, we use the Muller method to search out for all intrinsic values. The results showed that the highest order of spherical harmonic function for constructing regional model of fields is limited, thus high-resolution spherical harmonic structure of local gravity field need to be improved.

  Info
Periodical
Edited by
Han Zhao
Pages
3001-3005
DOI
10.4028/www.scientific.net/AMM.130-134.3001
Citation
J. Q. Wang, H. Y. Chen, Y. F. Chen, "The Analysis of the Associated Legendre Functions with Non-Integral Degree", Applied Mechanics and Materials, Vols. 130-134, pp. 3001-3005, 2012
Online since
October 2011
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