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On computing ellipsoidal harmonics using Jekeli's renormalization
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SYSNO ASEP 0388887 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On computing ellipsoidal harmonics using Jekeli's renormalization Author(s) Sebera, Josef (ASU-R) RID, ORCID
Bouman, J. (DE)
Bosch, W. (DE)Source Title Journal of Geodesy. - : Springer - ISSN 0949-7714
Roč. 86, č. 9 (2012), s. 713-726Number of pages 14 s. Language eng - English Country DE - Germany Keywords Earth's gravitational field ; spherical and ellipsoidal harmonics ; hypergeometric function Subject RIV BN - Astronomy, Celestial Mechanics, Astrophysics Institutional support ASU-R - RVO:67985815 UT WOS 000307556800003 DOI 10.1007/s00190-012-0549-4 Annotation Gravity data observed on or reduced to the ellipsoid are preferably represented using ellipsoidal harmonics instead of spherical harmonics. Ellipsoidal harmonics, however, are difficult to use in practice because the computation of the associated Legendre functions of the second kind that occur in the ellipsoidal harmonic expansions is not straightforward. Jekeli's renormalization simplifies the computation of the associated Legendre functions. We extended the direct computation of these functions-as well as that of their ratio-up to the second derivatives and minimized the number of required recurrences by a suitable hypergeometric transformation. Compared with the original Jekeli's renormalization the associated Legendre differential equation is fulfilled up to much higher degrees and orders for our optimized recurrences. Workplace Astronomical Institute Contact Radka Svašková, bibl@asu.cas.cz, Tel.: 323 620 326 Year of Publishing 2013
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