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Asymptotics for Gegenbauer-Sobolev orthogonal polynomials associated with non-coherent pairs of measures
(IOS Press, 2008-01-01)
Inner products of the type < f, g >(S) = < f, g >psi(0) + < f', g'>psi(1), where one of the measures psi(0) or psi(1) is the measure associated with the Gegenbauer polynomials, are usually referred to as Gegenbauer-Sobolev ...
Ultrastructural elliptical models
(CANADIAN JOURNAL STATISTICS, 1996)
Dolby's (1976) ultrastructural model with no replications is investigated within the class of the elliptical distributions. General asymptotic results are given for the sample covariance matrix S in the presence of incidental ...
Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case
(Elsevier B.V., 2012-11-01)
We investigate the location, monotonicity, and asymptotics of the zeros of the polynomials orthogonal with respect to the Sobolev type inner product< p, q > (lambda,c.j) = integral(b)(a) p(x)q(x)mu(x) + lambda p((j))(c)q ...
Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights
(Elsevier B.V., 2010-12-15)
We consider the Sobolev inner product< f.g > = integral(1)(-1) f(x)g(x)(1 - x(2))(alpha-1/2) dx + integral f'(x)g'(x)d psi(x), alpha > -1/2,where d(psi) is a measure involving a Gegenbauer weight and with mass points outside ...
Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case
(Elsevier B.V., 2012-11-01)
We investigate the location, monotonicity, and asymptotics of the zeros of the polynomials orthogonal with respect to the Sobolev type inner product< p, q > (lambda,c.j) = integral(b)(a) p(x)q(x)mu(x) + lambda p((j))(c)q ...
Asymptotic Scenarios for the Proton's Central Opacity: An Empirical Study
(Amer Inst Physics, 2015-01-01)
We present a model-independent analysis of the experimental data on the ratio X between the elastic and total cross-sections from pp and p (p) over bar scattering in the c.m. energy interval 5 GeV - 8 TeV. Using a novel ...
ASYMPTOTIC BEHAVIOUR OF JACOBI POLYNOMIALS AND THEIR ZEROS
(Amer Mathematical Soc, 2016-02-01)
We obtain the explicit form of the expansion of the Jacobi polynomial P-n((alpha, beta)) (1 - 2x/beta) in terms of the negative powers of beta. It is known that the constant term in the expansion coincides with the Laguerre ...
Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights
(Elsevier B.V., 2010-12-15)
We consider the Sobolev inner product< f.g > = integral(1)(-1) f(x)g(x)(1 - x(2))(alpha-1/2) dx + integral f'(x)g'(x)d psi(x), alpha > -1/2,where d(psi) is a measure involving a Gegenbauer weight and with mass points outside ...