Spherical harmonic coefficients of isotropic polynomial functions with applications to gravity field modelingSpherical harmonic coefficients of isotropic polynomial functions with applications to gravity field modeling Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2025-07-312023enVarious aspects of gravity field modeling rely upon analytical mathematical functions for calculating spherical harmonic coefficients. Such functions allow quick and efficient evaluation of cumbersome convolution integrals defined on the sphere. In this work, we present a new analytical method for determining spherical harmonic coefficients of isotropic polynomial functions. This method in computationally flexible and efficient, since it makes use of recurrence relations. Also, its use is universal and could be extended to piecewise polynomials and polynomials with compact support. Our numerical investigation of the proposed method shows that certain recurrence relations lose accuracy as the order of implemented polynomials increases because of accumulation of numerical errors. Propagation of these errors could be mitigated by hybrid methods or using extended precision arithmetic. We demonstrate the relevance of our method in gravity field modeling and discuss two areas of application. The first one is the design of B-spline windows and filter kernels for the low-pass filtering of gravity field functionals (e.g., GRACE Follow-On monthly geopotential solutions). The second one is the calculation of spherical harmonic coefficients of isotropic polynomial covariance functions.This work has been produced with the financial assistance of the European Union and the European Space Agency under the project FRM4S6 (Fiducial Reference Systems for Sentinel-6, No. 4000129892/20/NL/FF/ab).http://creativecommons.org/licenses/by/4.0/Journal of Geodesy9711Piretzidis_et_al_J. Geod._97(11)_2023.pdfChania [Greece]Library of TUC2025-07-31application/pdf6.0 MBfree Piretzidis Dimitrios Dimitrios Kotsakis Christopher Mertikas Stylianos Μερτικας Στυλιανος Sideris Michael G. Springer Recurrence relations Polynomials Isotropic filtering B-splines Covariance functions GRACE GRACE-FO