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Linear combinations of orthogonal polynomials generating positive quadrature formulas. (English) Zbl 0708.65022
Linear combinations of monic polynomials $$p_ k$$ of degree k orthogonal on [-1,1] with respect to the positive measure $$d\sigma$$ (x) are considered. Specifically, sufficient conditions on the real numbers $$\mu_ j$$, $$j=0,...,m$$ are given so that the sum $$\sum^{m}_{j=0}\mu_ jp_{n-j}$$ has n simple zeros in (-1,1) and the numerical interpolatory quadrature formula for integration with respect to $$d\sigma$$ (x) using these zeros as nodes has positive weights.
Reviewer: W.E.Smith

##### MSC:
 65D32 Numerical quadrature and cubature formulas 41A55 Approximate quadratures 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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##### References:
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