2014/05/09 by Toshio Fukushima · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · Mathematics · #Geophysics and Gravity Measurements #Solar and Space Plasma Dynamics #Geomagnetism and Paleomagnetism Studies #Physics #Prolate spheroid #Spherical harmonics #Prolate spheroidal coordinates #Gravitational field #Legendre polynomials #Associated Legendre polynomials #Legendre function #Harmonics #Field (mathematics) #Gravitation #Computation #Classical mechanics #Mathematical analysis #Quantum mechanics #Pure mathematics #Orthogonal polynomials #Mathematics #Algorithm
paper · pdf · doi:10.1088/0004-6256/147/6/152
openalex publication_date 2014/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
As a modification of the oblate spheroidal case, a recursive method is developed to compute the point value and a few low-order derivatives of the prolate spheroidal harmonics of the second kind, Q nm ( y ), namely the unnormalized associated Legendre function (ALF) of the second kind with its argument in the domain, 1 < y < ∞ . They are required in evaluating the prolate spheroidal harmonic expansion of the gravitational field in addition to the point value and the low-order derivatives of , the 4π fully normalized ALF of the first kind with its argument in the domain, | t | ⩽ 1. The new method will be useful in the gravitational field computation of elongated celestial objects.