Remarks on orthogonal polynomials with respect to varying measures and related problems
International Journal of Mathematics and Mathematical Sciences, 1993 We point out the relation between the orthogonal polynomials with respect to (w.r.t.) varying measures and the so-called orthogonal rationals on the unit circle in the complex plane.
Xin Li
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New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials
Mathematics, 2020 A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation ...
Luis E. Garza +2 more
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Determinant inequalities for sieved ultraspherical polynomials
International Journal of Mathematics and Mathematical Sciences, 2001 Paul Turan first observed that the Legendre polynomials satisfy the inequality Pn2(x)−Pn−1(x)Pn(x)>0 ...
J. Bustoz, I. S. Pyung
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Design of Nonuniformly Spaced Antenna Arrays Using Orthogonal Coefficients Equating Method [PDF]
Radioengineering, 2022 Orthogonal Coefficients Equating (OCE) method as an analytic method is proposed to synthesize nonuniformly spaced antenna arrays to have array factors nearly equal to that of a previously designed uniformly spaced antenna arrays.
M. Khalaj-Amirhosseini
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Polynomial and rational measure modifications of orthogonal polynomials via infinite-dimensional banded matrix factorizations [PDF]
, 2023 Timon S. Gutleb +2 more
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A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND \(q\)-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Ural Mathematical Journal, 2023 In this paper, we consider the following \(\mathcal{L}\)-difference equation $$\Phi(x) \mathcal{L}P_{n+1}(x)=(\xi_nx+\vartheta_n)P_{n+1}(x)+\lambda_nP_{n}(x),\quad n\geq0,$$where \(\Phi\) is a monic polynomial (even), \(\deg\Phi\leq2\), \(\xi_n ...
Yahia Habbachi
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On 2-orthogonal polynomials of Laguerre type
International Journal of Mathematics and Mathematical Sciences, 1999 Let {Pn}n≥0 be a sequence of 2-orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let {Qn}n≥0 be the sequence of polynomials defined by Qn:=(n+1)−1P′n+1,n≥0.
Khalfa Douak
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Szegő polynomials: some relations to L-orthogonal and orthogonal polynomials
Journal of Computational and Applied Mathematics, 2003 The authors consider the Szegö polynomials \(S_n(z)\) with real reflection coefficients and obtain some relations to certain self-inverse orthogonal \(L\)-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on a real line. The polynomials obtained by rotating the coefficients in the recursive relations satisfied by
Bracciali, Cleonice Fátima +2 more
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Recurrence Relations for Orthogonal Polynomials on Triangular Domains
Mathematics, 2016 In Farouki et al, 2003, Legendre-weighted orthogonal polynomials P n , r ( u , v , w ) , r = 0 , 1 , … , n , n ≥ 0 on the triangular domain T = { ( u , v , w ) : u , v , w ≥ 0 , u + v + w = 1 } are constructed, where u , v , w
Abedallah Rababah
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Solving change of basis from Bernstein to Chebyshev polynomials
Examples and CounterexamplesWe provide two closed-form solutions to the change of basis from Bernstein polynomials to shifted Chebyshev polynomials of the fourth kind and show them to be equivalent by applying Zeilberger’s algorithm. The first solution uses orthogonality properties
D.A. Wolfram
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