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Derivation of Inverse Expansions for Auxiliary Latitudes by Hermite Interpolation Method

LI Houpu1 BIAN Shaofeng1,2(1 Department of Navigation,Naval University of Engineering,717 Jiefang Road,Wuhan 430033,China)(2 Institute of Geodesy and Geophysics,Chinese Academy of Sciences,340 Xudong Road,Wuhan 430077,China)  
Both forward and inverse formulas between auxiliary and geodetic latitudes are derived with the help of computer algebra system in a comprehensive way;and also some mistakes that once were made in the high orders of previous forward formulas are pointed out and corrected.New symbolic expressions of the inverse expansions for these auxiliary latitudes are systematically given in virtue of Hermite interpolation.Their coefficients are expressed in a power series of the eccentricity e,which makes the expansions more uniform.
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