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Spline approximations to spherically symmetric distributions. (English) Zbl 0586.41009
We discuss the problem of approximating a function f of the radial distance r in $${\mathbb{R}}^ d$$ on $$0\leq r<\infty$$ by a spline function of degree m with n (variable) knots. The spline is to be constructed so as to match the first 2n moments of f. We show that if a solution exists, it can be obtained from an n-point Gauss-Christoffel quadrature formula relative to an appropriate moment functional or, if f is suitably restricted, relative to a measure, both depending on f. The moment functional and the measure may or may not be positive definite. Pointwise convergence is discussed as $$n\to \infty$$. Examples are given including distributions from statistical mechanics.

##### MSC:
 41A15 Spline approximation 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
EISPACK; LINPACK
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##### References:
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