A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas
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2013-01-01
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Resumo
The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.
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Hypergeometric polynomials, Para-orthogonal polynomials, Quadrature rules, Extremal, Gaussian type quadrature, Orthogonal property, Quadrature formula, Unit circles, Computational methods, Mathematical techniques, Polynomials
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Applied Numerical Mathematics, v. 65, p. 41-52.