Pade Approximants for Geodesy
Mathematical Physics
2026-05-06 v1 math.MP
Abstract
In this note we analyze the use of Pad\'e approximants for downward continuation beyond the radius of convergence of spherical harmonic expansions (SHEs), and for identifying the complex singularities of the gravitational potential. SHEs are, in essence, expansions in 1/r, i.e., expansions about the point at infinity. Their domain of convergence is generically the exterior of the Brillouin sphere. However, for synthetic models with analytic topography and density the region of convergence may be larger, with the deviation decreasing as the structural complexity of the planet increases.
Cite
@article{arxiv.2605.04027,
title = {Pade Approximants for Geodesy},
author = {Ovidiu Costin and Gerald V. Dunne and Crichton Ogle},
journal= {arXiv preprint arXiv:2605.04027},
year = {2026}
}
Comments
19 pages, 11 figures