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DOE OSTI · 2234057

Isotropic N-point basis functions and their properties

Cahn, Robert N.·Slepian, Zachary
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Abstract

Isotropic functions of positions r 1 , r 2 ,..., r N , i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch–Gordan coefficients. An orthonormal basis of such functions provides a formalism suitable for analyzing isotropic distributions such as those that arise in cosmology, for instance in the clustering of galaxies as revealed by large-scale structure surveys. The algebraic properties of the basis functions are conveniently expressed in terms of 6-j and 9-j symbols. Finally, the calculation of relations among the basis functions is facilitated by 'Yutsis' diagrams for the addition and recoupling of angular momenta.

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97 MATHEMATICS AND COMPUTING

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Cahn, Robert N., Slepian, Zachary. 2023-07-21. Isotropic N-point basis functions and their properties. https://doi.org/10.1088/1751-8121%2Facdfc4

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