31. The rotational behavior of the spherical harmonics is perhaps their quintessential feature from the viewpoint of group theory. 32. On the unit sphere, this is equivalent to integrating all spherical harmonics up to the same order. 33. In " n "-dimensional Euclidean space, zonal spherical harmonics are defined as follows. 34. The following is a compact account of the spherical harmonics used to model Earth's gravitational field. 35. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. 36. Alternatively, this equation follows from the relation of the spherical harmonic functions with the Wigner D-matrix. 37. Each of these modes can be mathematically represented by a spherical harmonic of degree l and azimuthal order m. 38. Ren Ng extended this work to handle higher frequency shadows by replacing spherical harmonics with non-linear wavelets. 39. Some prose in the book is written in the shape of the sinusoidal functions found in the spherical harmonics . 40. The equations for the p x and p y orbitals depend on the phase convention used for the spherical harmonics .
