A Simple Method for Deriving the Transformation Formula of Spherical Harmonic Expansion Coefficients and its Application

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  • 球関数展開係数の座標変換による変換式の簡単な導出法とその応用
  • キュウ カンスウ テンカイ ケイスウ ノ ザヒョウ ヘンカン ニ ヨル ヘンカ

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Suppose an arbitrary function expressed in a surface spherical harmonic expansion series when the pole is translocated at an arbitrary point on the surface of a sphere. The coefficients of the expansion series are functions of the latitude and longitude of the translocated pole. GANEKO [6] has derived the general transformation formula of spherical harmonic expansion coefficients in a form of the modified Jacobi polynomials. It can be applied to theoretical problems of geodesy and geophysics including the translocation of the polar axis. This paper shows a simple method for deriving GANEKO's transformation formula and its inverse one, with their applications to the global geoidal height.

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