| 41. | In seismology, the Laplace spherical harmonics are generally defined as ( this is the convention used in this article)
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| 42. | Spaces of spin-weighted spherical harmonics were first identified in connection with the representation theory of the Lorentz group.
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| 43. | In many cases different linear combinations of spherical harmonics are chosen to construct a cubic f-orbital basis set.
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| 44. | Where the " L " is a result of the parity of the corresponding spherical harmonic of the wavefunction.
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| 45. | Many aspects of the theory of Fourier series could be generalized by taking expansions in spherical harmonics rather than trigonometric functions.
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| 46. | Any smooth complex-valued function on a sphere can be written as a weighted sum of the spherical harmonic functions.
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| 47. | SPHARM-PDM is a tool that computes point-based models using a parametric boundary description based on spherical harmonics.
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| 48. | Analyses of the Earth's magnetic field use a modified version of the usual spherical harmonics that differ by a multiplicative factor.
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| 49. | In the same year, P-wave data were used to determine 150 spherical harmonic coefficients for velocity anomalies in the mantle.
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| 50. | In particular, he authored an important treatise on spherical harmonics and Legendre functions ( " Handbuch der Kugelfunctionen " ).
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