Abstract
A complete series solution of Molodensky's boundary-value problem is derived using, instead of an integral equation, analytical continuation by means of power series. This solution is shown to be equivalent, term by term, to the Molodensky-Brovar series, but is simpler and practically more convenient.
Résumé
On déduit une série qui donne une solution complète du problème de Molodensky, en utilisant, au lieu d'une équation intégrale, la continuation analytique par une série de puissances. Il s'ensuit que cette solution est équivalente à la série de Molodensky-Brovar, mais elle est plus simple et plus pratique.
Zusammenfassung
Eine vollständige Reihenlösung des Problems von Molodensky wird hergeleitet, wobei anstatt einer Integralgleichung die analytische Fortsetzung mittels Potenzreihen zugrunde gelegt wird. Es zeigt sich, dass diese Lösung gliedweise äquivalent zur Reihe von Molodensky-Brovar ist, aber sie ist einfacher und praktisch brauchbarer.
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References
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Moritz, H. A new series solution of Molodensky's problem. Bull. Geodesique 96, 183–195 (1970). https://doi.org/10.1007/BF02521707
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DOI: https://doi.org/10.1007/BF02521707