Tittle: Analytical equations for an infinite series involving low‑order associated Legendre functions in geoscience
Abstract: The associated Legendre functions constituting the kernel function of spherical harmonics have a wide range of applications in geodesic and geophysical fields, such as calculating the Green’s functions for a spherical Earth model. The analytical expressions for the infinite series involving the associated Legendre functions are useful. In this paper, starting with the generating function, we present a set of analytical equations for an infinite series involving associated low-order \(\left( {m = 0,~1,~2} \right)\) Legendre functions. After careful verification, the accuracy and effectiveness of the nearly sixty listed equations are confirmed.
Citation:Tang, H., Sun, W. Analytical equations for an infinite series involving low-order associated Legendre functions in geoscience. J Geod 95, 86 (2021).
