Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions,
OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE AND SURVEYING
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A technique is developed for generating spherical harmonics by exact computation in integer mode thereby circumventing any source of rounding errors. Essential results of the theory of spherical harmonics are recapitulated by intrinsic properties of the space of homogeneous harmonic polynomials. Exact computation of maximal linearly independent and orthonormal systems of spherical harmonics is explained using exclusively integer operations. The numerical efficiency is discussed. The development of exterior gravitational potential in a series of outer spherical harmonics is investigated. Some numerical examples are given for solving exterior Dirichlets boundary-value problems by use of outer spherical harmonic expansions for not-necessarily spherical boundaries. Keywords Homogeneous harmonic polynomials Spherical harmonics Exact computation in integer mode Series expansion into spherical harmonics Exterior dirichlets problem.
- Theoretical Mathematics