Journal ArticleDOI
An introduction to orthogonal polynomials
About:
This article is published in Mathematics of Computation.The article was published on 1981-01-01. It has received 3151 citations till now. The article focuses on the topics: Orthogonal polynomials & Classical orthogonal polynomials.read more
Citations
More filters
Journal ArticleDOI
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
TL;DR: This work represents the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error.
Posted Content
The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
Roelof Koekoek,René F. Swarttouw +1 more
TL;DR: The Askey-scheme of hypergeometric orthogonal polynomials was introduced in this paper, where the q-analogues of the polynomial classes in the Askey scheme are given.
Journal ArticleDOI
Modeling uncertainty in flow simulations via generalized polynomial chaos
TL;DR: In this paper, the authors present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations, which is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as trial basis to represent the random space.
Journal ArticleDOI
Shape fluctuations and random matrices
TL;DR: In this article, the authors studied a random growth model in two dimensions closely related to the one-dimensional totally asymmetric exclusion process and showed that the shape fluctuations, appropriately scaled, converges in distribution to the Tracy-Widom largest eigenvalue distribution for the Gaussian Unitary Ensemble (GUE).
Book
Orthogonal Polynomials of Several Variables
Charles F. Dunkl,Yuan Xu +1 more
TL;DR: In this article, the authors considered the properties of orthogonal polynomials on the unit sphere, root systems and Coxeter groups, and the Summability of Orthogonal expansions.