Results 41 to 50 of about 61,972 (313)
On zeros of discrete orthogonal polynomials
Journal of Approximation Theory, 2009 The authors establish sharp inequalities for the extreme zeros of the classical discrete orthogonal polynomials: Charlier, Krawtchouk, Meixner, and Hahn. Their approach is based on the corresponding difference equations. For Charlier, Krawtchouk, and Meixner polynomials the function bounding the zero spacing is unimodal, meanwhile for the Hahn case ...
Krasikov, Ilia, Zarkh, Alexander
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On the analytic form of the discrete Kramer sampling theorem
International Journal of Mathematics and Mathematical Sciences, 2001 The classical Kramer sampling theorem is, in the subject of self-adjoint boundary value problems, one of the richest sources to obtain sampling expansions. It has become very fruitful in connection with discrete Sturm-Liouville problems.
Antonio G. García +2 more
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A Probablistic Origin for a New Class of Bivariate Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2008 We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an ...
Michael R. Hoare, Mizan Rahman
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Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials
IEEE Access, 2023 Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials and used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision.
Basheera M. Mahmmod +4 more
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Exactly solvable discrete quantum mechanical systems and multi-indexed orthogonal polynomials of the continuous Hahn and Meixner–Pollaczek types [PDF]
, 2019 We present new exactly solvable systems of the discrete quantum mechanics with pure imaginary shifts, whose physical range of the coordinate is the whole real line.
S. Odake
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Some discrete d-orthogonal polynomial sets
Journal of Computational and Applied Mathematics, 2003 The concept of \(d\)-orthogonality has been received quite a lot of attention over the last ten years and the authors give a very interesting contribution to the development of the field. Let \(u\) be a linear functional on the space \textbf{P} of all polynomials; its action is written as \(\langle u,f\rangle\) for all \(f\in\mathbf{P}\).
Ben Cheikh, Yousséf, Zaghouani, Ali
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Stable Calculation of Krawtchouk Functions from Triplet Relations
Mathematics, 2021 Deployment of the recurrence relation or difference equation to generate discrete classical orthogonal polynomials is vulnerable to error propagation. This issue is addressed for the case of Krawtchouk functions, i.e., the orthonormal basis derived from ...
Albertus C. den Brinker
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On Generating Orthogonal Polynomials for Discrete Measures
Zeitschrift für Analysis und ihre Anwendungen, 1998 In the present paper, we derive an algorithm for computing the recurrence coefficients of orthogonal polynomials with respect to discrete measures. This means that the support of the measure is a finite set. The algorithm is based oniormulae of Nevai describing the transformation of recurrence coefficients, if we add a point mass to the measure of ...
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New Characterizations of Discrete Classical Orthogonal Polynomials
Journal of Approximation Theory, 1997 In this very nice paper, the authors consider (quasi)orthogonal polynomial sequences [\((Q)OPS\): see (i)] with respect to a regular moment functional \(\sigma\) [see (ii)]. (i) \(\{P_n\}_{n=0}^{\infty}\) polynomials in \(x\) with degree \(P_n=n,\;n\geq 0\) form a \(QOPS\) resp. \(OPS\) if \(\langle \sigma,P_nP_m\rangle = K_n\delta_{nm}\) with \(K_n\in{
Kwon, KH Kwon, Kil Hyun +2 more
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Discrete orthogonal polynomials associated with Macdonald functions
The Ramanujan Journal, 2022 New sequences of discrete orthogonal polynomials associated with the modified Bessel function $K_ (z)$ or Macdonald function are considered. The corresponding weight function is $ ^k _{k+ +1}(t)/ k!$, where $\ k \in \mathbb{N}_0, \ t \ge 0,\ > -1,\ 0 < < 1,\ _ (z) = 2 z^{ /2} K_ \left( 2\sqrt z\right)$.
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