3 Generalized Spherical Harmonics
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Expressing Crystallographic Textures through the Orientation Distribution Function: Conversion between the Generalized Spherical Harmonic and Hyperspherical Citation
In the analysis of crystallographic texture, the orientation distribution function of the grains is generally expressed as a linear combination of the generalized spherical harmonics. Recently, an alternative expansion of the orientation distribution function—as a linear combination of the hyperspherical harmonics—has been proposed, with the advantage that this is a function of the angles that ...
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Biological rhythms such as circadian rhythms, biochemical rhythms and neural oscillators are based on the mathematical model of the theory of harmonic oscillators. These are solutions of certain second-order differential equations. They can also be viewed as spherical harmonics on the circle in the two-dimensional Euclidean space. The spherical harmonics on (n-1)-spheres and, more generally, th...
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In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when...
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Spherical harmonics in an arbitrary dimension are employed widely in quantum theory. Spherical harmonics are also called hyperspherical harmonics when the dimension is larger than 3. In this paper, we derive some integral identities involving spherical harmonics in an arbitrary dimension.
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