11. For the sphere, for example, the eigenfunctions are the spherical harmonics . 12. The end of the century also saw a very detailed discussion of spherical harmonics . 13. It is an issue of numerical integration with special functions ( Spherical Harmonics ). 14. The angular portions of the solutions to such equations take the form of spherical harmonics . 15. An efficient method must be used to encode this data, such as spherical harmonics . 16. The spherical harmonics are derived from the approach of looking for harmonic functions of the form 17. :You might have better luck searching for discussions of the spherical harmonic differential equation. 18. I'm trying to normalize Associated Legendre polynomials to turn them into Spherical harmonics . 19. Spherical harmonics can represent any scalar field ( function of position ) that satisfies certain properties.20. The spherical harmonics turn out to be critical to practical solutions of Laplace's equation.
