scispace - formally typeset
Search or ask a question
Topic

Difference polynomials

About: Difference polynomials is a research topic. Over the lifetime, 7911 publications have been published within this topic receiving 120549 citations.


Papers
More filters
Book
01 Oct 1991
TL;DR: In this article, the orthogonality relation (2.0.1) is reduced to 2.0, where w(x) is a function of jumps, i.e. the piecewise constant function with jumps ϱ i at the points x = x i.
Abstract: The basic properties of the polynomials p n (x) that satisfy the orthogonality relations $$ \int_a^b {{p_n}(x)} {p_m}(x)\rho (x)dx = 0\quad (m e n) $$ (2.0.1) hold also for the polynomials that satisfy the orthogonality relations of a more general form, which can be expressed in terms of Stielties integrals $$ \int_a^b {{p_n}(x)} {p_m}(x)dw(x) = 0\quad (m e n), $$ (2.0.2) where w(x) is a monotonic nondecreasing function (usually called the distribution function). The orthogonality relation (2.0.2) is reduced to (2.0.1) in the case when the function w(x) has a derivative on (a, b) and w′(x) = ϱ(x). For solving many problems orthogonal polynomials are used that satisfy the orthogonality relations (2.0.2) in the case when w(x) is a function of jumps, i.e. the piecewise constant function with jumps ϱ i at the points x = x i . In this case the orthogonality relation (2.0.2) can be rewritten in the form $$ \sum\limits_i {{p_n}({x_i})pm} ({x_i}){\rho_i} = 0\quad (m e n). $$ (2.0.3)

1,032 citations

Book
01 Jan 2002

889 citations

Journal ArticleDOI

817 citations

Journal ArticleDOI
TL;DR: In this article, a family of orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type was studied.
Abstract: We study a family of "classical" orthogonal polynomials which satisfy (apart from a 3-term recurrence relation) an eigenvalue problem with a differential operator of Dunkl-type. These polynomials can be obtained from the little $q$-Jacobi polynomials in the limit $q=-1$. We also show that these polynomials provide a nontrivial realization of the Askey-Wilson algebra for $q=-1$.

775 citations

MonographDOI
01 Jun 1994
TL;DR: General concept of polynomials elementary inequalities zeros of poynomials special classes of polynnomials extremal problems for polynmials inequalities connected with trigonometric sums are introduced.
Abstract: General concept of polynomials elementary inequalities zeros of polynomials special classes of polynomials extremal problems for polynomials inequalities connected with trigonometric sums.

508 citations


Network Information
Related Topics (5)
Polynomial
52.6K papers, 853.1K citations
90% related
Operator theory
18.2K papers, 441.4K citations
89% related
Bounded function
77.2K papers, 1.3M citations
88% related
Lipschitz continuity
20.8K papers, 382.6K citations
88% related
Banach space
29.6K papers, 480.1K citations
87% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202365
2022132
202121
202022
201917
201837