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标题：Convergence of spherical harmonic series expansion of the Earth’s gravitational potential
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作者：Wenbin Shen
期刊名称：Geo-spatial Information Science
印刷版ISSN：1009-5020
电子版ISSN：1993-5153
出版年度：2009
卷号：12
期号：1
页码：1-6
DOI：10.1007/s11806-009-0180-6
出版社：Taylor and Francis Ltd
摘要：Given a continuous boundary value on the boundary of a “simply closed surface” ∂S that encloses the whole Earth, a regular harmonic fictitious field V*(P) in the domain outside an inner sphere Ki that lies inside the Earth could be determined, and it is proved that V*(P) coincides with the Earth’s real field V(P) in the whole domain outside the Earth. Since in the domain outside the inner sphere Ki and the fictitious regular harmonic function V*(P) could be expressed as a uniformly convergent spherical harmonic series, it is concluded that the Earth’s potential field could be expressed as a uniformly convergent spherical harmonic expansion series in the whole domain outside the Earth.
关键词：potential field; fictitious field; uniqueness of the solution; spherical harmonic series; uniform convergence