Related papers: Peakons and Cauchy Biorthogonal Polynomials
In the 6th Int. Symposium on OPSFA there were several communications dealing with concrete applications of orthogonal polynomials to experimental and theoretical physics, chemistry, biology and statistics. Here I make suggestions concerning…
This paper has been withdrawn because it has been by far superseded by the Author's post arXiv:1108.1306v6, which was published on 30/08/2011.
This paper presents a closed form polynomial expression for the binary cyclotomic polynomial. We contrast this against expressions for binary cyclotomic polynomials in (Lam and Leung 1996) and (Lenstra 1979).
The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a…
This paper has been withdrawn by the author due to a serious flaw that needs to be fixed. That is in progress by the author.
This submission has been withdrawn by the authors because it is a duplicate of arXiv:hep-ph/0611336. It was due to a technical submission error by the authors.
This paper has been superseded by gr-qc/0611101.
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
In the present article, we have given a corrigendum to our paper ``On (p,q)-analogue of Bernstein operators" published in Applied Mathematics and Computation 266 (2015) 874-882.
The duality triads were defined in the preceding paper.(ArXiv: math.GM/0402260 v 1 Feb. 2004). Notation, enumeration of formulas and references is therefore to be continued hereby. In this paper Fibonomial triangle and further Pascal-like…
This is the full version of "Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results" appearing on this server and also…
The Cauchy polynomials with a $q$ parameter were recently defined, and several arithmetical properties were studied. In this paper, we establish explicit formulae for computing the Cauchy polynomials with a $q$ parameter in terms of…
This paper has been superseded by hep-ph/0510352.
The idea of this review article is to discuss in a unified way the orthogonality of all positive definite polynomial solutions of the $q$-hypergeometric difference equation on the $q$-linear lattice by means of a qualitative analysis of the…
In hep-ph/0404212 Diakonov, Petrov, and Polyakov respond to my recent comments on their 1997 paper, ``Exotic anti-decuplet of baryons: prediction from chiral solitons''. Their responses do not address the basic issues or alter the…
The Darboux transformations of Krawtchouk polynomials are investigated and all possible exceptional Krawtchouk polynomials obtainable from a single-step Darboux transformation are considered. The properties of these exceptional Krawtchouk…
In this paper, we consider higher-order Bernoulli and poly-Bernoulli mixed type polynomials and we give some interesting identities of those polynomials arising from umbral calculus.
This is basically the update of [arXiv:0809.1869], a review on charmed baryon physics around 2007. Topics of this review include the spectroscopy, strong decays, lifetimes, nonleptonic and semileptonic weak decays, and electromagnetic…
We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for…
An improved (streamlined and extended) version of this paper is available as math.RA/0203010, which however omits some details. We recommend the later version unless details are essential.