Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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An application of the multivariate Lagrange-Bürmann expansion in mathematical geodesy


Authors: P. Henrici and G. R. Wilkens
Journal: Quart. Appl. Math. 45 (1987), 165-172
MSC: Primary 86A30
DOI: https://doi.org/10.1090/qam/885178
MathSciNet review: 885178
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Abstract: In the simplified model of geodesy where the earth is conceived as a rotational ellipsoid, if the eccentricity of the ellipsoid is to be determined from gravity measurements, an equation of the form $ y = x - zh\left( x \right)$ is to be solved for $ x$, where $ y$ and $ z$ are small parameters whose values can be measured and $ h$ is a known function. We obtain the expansion of $ x$ in powers of $ y$ and $ z$ by means of the general Lagrange--Bürmann formula.


References [Enhancements On Off] (What's this?)

  • [1] J. C. Alexander, The numerics of computing geodetic ellipsoids, SIAM Rev. 27 (1985), no. 2, 241–247. MR 792455, https://doi.org/10.1137/1027056
  • [2] B. W. Char, K. O. Geddes, G. H. Gonnet, and S. M. Watt, Maple user's manual, 3rd ed., Univ. of Waterloo Res. Rep. CS-83-41 (1983)
  • [3] P. Henrici, Die Lagrange-Bürmannsche Formel bei formalen Potenzreihen, Jahresber. Deutsch. Math.-Verein. 86 (1984), no. 4, 115–134 (German). MR 766156
  • [4] W. A. Hieskanen and H. Moritz, Physical geodesy, Freeman, San Francisco, 1966

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DOI: https://doi.org/10.1090/qam/885178
Article copyright: © Copyright 1987 American Mathematical Society


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