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Discrete approximations to spherically symmetric distributions. (English) Zbl 0508.65012

MSC:
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
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References:
[1] Calder, A.C., Laframboise, J.G., Stauffer, A.D.: Optimum step-function approximation of the Maxwell distribution (unpublished)
[2] Galant, D.: Gauss quadrature rules for the evaluation of \(2\pi ^{ - \tfrac{1}{2}} \int\limits_0^\infty {\exp ( - x^2 )f(x)dx} \) . Math. Comput.23 (1969), Review42, 676-677. Loose microfiche suppl. E · doi:10.2307/2004399
[3] Galant, D.: An implementation of Christoffel’s theorem in the theory of orthogonal polynomials. Math. Comput.25, 111-113 (1971) · Zbl 0219.65017
[4] Gautschi, W.: A survey of Gauss-Christoffel quadrature formulae. In: E.B. Christoffel, The Influence of his Work on Mathematics and the Physical Sciences (P.L. Butzer, F. Feh?r, eds.), pp. 72-147. Basel: Birkh?user 1981 · Zbl 0479.65001
[5] Gautschi, W.: On generating orthogonal polynomials. SIAM J. Sci. Statist. Comput.3, 289-317 (1982) · Zbl 0482.65011 · doi:10.1137/0903018
[6] Gautschi, W.: An algorithmic implementation of the generalized Christoffel theorem. In: Numerische Integration (G. H?mmerlin, ed.), pp. 89-106. Intern. Ser. Numer. Math. 57. Basel: Birkh?user 1982 · Zbl 0518.65006
[7] Gautschi, W., Milovanovi?, G.V.: Gaussian quadrature involving Einstein and Fermi functions with an application to convergence acceleration of series, submitted for publication. · Zbl 0576.65012
[8] Hildebrand, F.B.: Introduction to Numerical Analysis, 2nd ed., New York: McGraw-Hill 1974 · Zbl 0279.65001
[9] Laframboise, J.G., Stauffer, A.D.: Optimum discrete approximation of the Maxwell distribution. AIAA Journal7, 520-523 (1969) · doi:10.2514/3.5139
[10] Szeg?, G.: Orthogonal Polynomials, AMS Colloq. Publications, Vol.23, 4th ed. 2nd printing. Providence, R.I.: Amer. Math. Soc. 1978 · JFM 65.0278.03
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