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