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A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas
(2013-01-01)
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 ...
A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas
(2013-01-01)
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 ...
Rational approximations of the Arrhenius integral using Jacobi fractions and gaussian quadrature
(Springer, 2009-03-01)
The aim of this work is to find approaches for the Arrhenius integral by using the n-th convergent of the Jacobi fractions. The n-th convergent is a rational function whose numerator and denominator are polynomials which ...
Rational approximations of the Arrhenius integral using Jacobi fractions and gaussian quadrature
(Springer, 2009-03-01)
The aim of this work is to find approaches for the Arrhenius integral by using the n-th convergent of the Jacobi fractions. The n-th convergent is a rational function whose numerator and denominator are polynomials which ...
Orthogonality of quasi-orthogonal polynomials
(2018-01-01)
A result of Pólya states that every sequence of quadrature formulas Q n (f) with n nodes and positive Cotes numbers converges to the integral I(f) of a continuous function f provided Q n (f) = I(f) for a space of algebraic ...
APPROXIMATE CALCULATION OF SUMS II: GAUSSIAN TYPE QUADRATURE
(Siam Publications, 2016-01-01)
The present paper is a continuation of a recent article [SIAM T. Numer. Anal., 52 (2014), pp. 1867-1886], where we proposed an algorithmic approach for approximate calculation of sums of the form Sigma(N)(j=1) f (j). The ...
APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS
(Siam Publications, 2014-01-01)
Let N be a positive integer and x(j) be N equidistant points. We propose an algorithmic approach for approximate calculation of sums of the form Sigma(N)(j=1) F(x(j)). The method is based on the Gaussian type quadrature ...
APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS
(Siam Publications, 2015)