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On computing ellipsoidal harmonics using Jekeli's renormalization

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    0388887 - ASÚ 2013 RIV DE eng J - Journal Article
    Sebera, Josef - Bouman, J. - Bosch, W.
    On computing ellipsoidal harmonics using Jekeli's renormalization.
    Journal of Geodesy. Roč. 86, č. 9 (2012), s. 713-726. ISSN 0949-7714
    Institutional support: RVO:67985815
    Keywords : Earth's gravitational field * spherical and ellipsoidal harmonics * hypergeometric function
    Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics
    Impact factor: 2.808, year: 2012

    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.
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