Results 71 to 80 of about 351,291 (192)
A Unified Approach to Computing the Zeros of Orthogonal Polynomials
Journal of New Theory, 2023 We present a unified approach to calculating the zeros of the classical orthogonal polynomials and discuss the electrostatic interpretation and its connection to the energy minimization problem. This approach works for the generalized Bessel polynomials,
Ridha Moussa, James Tipton
doaj +1 more source
Using $\D$-operators to construct orthogonal polynomials satisfying higher order difference or differential equations [PDF]
, 2013 We introduce the concept of $\D$-operators associated to a sequence of polynomials $(p_n)_n$ and an algebra $\A$ of operators acting in the linear space of polynomials.
Durán, Antonio J.
core
On extreme zeros of classical orthogonal polynomials
Journal of Computational and Applied Mathematics, 2006 Let $x_1$ and $x_k$ be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree $k.$ We shall establish sharp inequalities of the form $x_1 B,$ which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical ...
openaire +3 more sources
Zero distribution of sequences of classical orthogonal polynomials
Abstract and Applied Analysis, 2003 We obtain the zero distribution of sequences of classical orthogonal polynomials associated with Jacobi, Laguerre, and Hermite weights. We show that the limit measure is the extremal measure associated with the corresponding weight.
Plamen Simeonov
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Semi-classical Laguerre polynomials and a third order discrete integrable equation
, 2009 A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main example we use is
Christoffel E B +12 more
core +3 more sources
Complex versus real orthogonal polynomials of two variables [PDF]
arXiv, 2013 Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples.
arxiv
A characterization of the four Chebyshev orthogonal families
International Journal of Mathematics and Mathematical Sciences, 2005 We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear ...
E. Berriochoa +2 more
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Orthogonal polynomials related to the unit circle and differential-difference equations [PDF]
Rendiconti di Matematica e delle Sue Applicazioni, 1997 In this paper we obtain the orthogonal polynomial sequences, related to the unit circle, that verify the following differential-difference equation: (z − α)(z − β)φ'_n(z)/n = (z + αn)φ_n(z) + β_nφ_{n−1}(z) .
A. Cachafeiro, C. Suárez
doaj
Tridiagonal Operators and Zeros of Polynomials in Two Variables
Abstract and Applied Analysis, 2016 The aim of this paper is to connect the zeros of polynomials in two variables with the eigenvalues of a self-adjoint operator. This is done by use of a functional-analytic method.
Chrysi G. Kokologiannaki +2 more
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Surveys in Approximation Theory, 1 (2005), 70-125, 2005 In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.
arxiv