On one set of orthogonal harmonic polynomials
نویسندگان
چکیده
منابع مشابه
On orthogonal polynomials related to arithmetic and harmonic sequences
In this paper we study special systems of orthogonal polynomials on the unit circle. More precisely, with a view to the recurrence relations fulfilled by these orthogonal systems, we analyze a link of non-negative arithmetic to harmonic sequences as a main subject. Here, arithmetic sequences appear as coefficients of orthogonal polynomials and harmonic sequences as corresponding Szegő parameters.
متن کاملDuality of Orthogonal Polynomials on a Finite Set
We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial ensemble. Introduction This note is about a certain duality of orthogonal polynomials defined on a finite set. If the weights of two systems of orthogonal p...
متن کاملChromatic Harmonic Indices and Chromatic Harmonic Polynomials of Certain Graphs
In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...
متن کاملOn Orthogonal Matrix Polynomials
In this paper we deal with orthogonal matrix polynomials. First of all, we establish some basic notations and results we need later. A matrix polynomial P is a matrix whose entries are polynomials, or, equivalently, a combination P(t) = A 0 +A 1 t+ +A n t n , where A 0 ; ; A n are numerical matrices (the size of all the matrices which appear in this paper is N N). A positive deenite matrix of m...
متن کاملOn Co-recursive Orthogonal Polynomials
is equivalent to (1.1) with 6„ = 0 (w^2) and Pi(0)p^0. The condition b„ = 0 (w^2) suggests the symmetric case, (i.e.,P„( — x) = ( —l)"P„(x)) but this is denied by the condition Pi(0) ^0. (In fact, (1.2) shows that Pn( — r)^0 whenever Pn(r)=0.) It then seems natural to ask what relations exist between a set of polynomials satisfying (1.2) and the corresponding symmetric polynomials which would b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-05019-9