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Discrete approximations to spherically symmetric distributions

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Summary

We consider the approximation of spherically symmetric distributions in ℝd by linear combinations of Heaviside step functions or Dirac delta functions. The approximations are required to faithfully reproduce as many moments as possible. We discuss stable methods of computing such approximations, taking advantage of the close connection with Gauss-Christoffel quadrature. Numerical results are presented for the distributions of Maxwell, Bose-Einstein, and Fermi-Dirac.

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Authors and Affiliations

  1. Department of Computer Sciences, Purdue University, Mathematical Sciences Building, Room 442, 47907, West Lafayette, Indiana, USA

    Walter Gautschi

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  1. Walter Gautschi
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Dedicated to Fritz Bauer on the occasion of his 60th birthday

Work supported in part by the National Science Foundation under Grant MCS-7927158A1

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Gautschi, W. Discrete approximations to spherically symmetric distributions. Numer. Math. 44, 53–60 (1984). https://doi.org/10.1007/BF01389754

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  • DOI: https://doi.org/10.1007/BF01389754

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