Results 51 to 60 of about 40,909 (200)

Jacobi-weighted orthogonal polynomials on triangular domains

Journal of Applied Mathematics, 2005
We construct Jacobi-weighted orthogonal polynomials 𝒫n,r(α,β,γ)(u,v,w),α,β,γ>−1,α+β+γ=0, on the triangular domain T. We show that these polynomials 𝒫n,r(α,β,γ)(u,v,w) over the triangular domain T satisfy the following properties: 𝒫n,r(α,β,γ)(u,v,w)∈ℒn,n ...
A. Rababah, M. Alqudah
doaj   +1 more source

Free energy expansions of a conditional GinUE and large deviations of the smallest eigenvalue of the LUE

Communications on Pure and Applied Mathematics, Volume 78, Issue 12, Page 2247-2304, December 2025.
Abstract We consider a planar Coulomb gas ensemble of size N$N$ with the inverse temperature β=2$\beta =2$ and external potential Q(z)=|z|2−2clog|z−a|$Q(z)=|z|^2-2c \log |z-a|$, where c>0$c>0$ and a∈C$a \in \mathbb {C}$. Equivalently, this model can be realised as N$N$ eigenvalues of the complex Ginibre matrix of size (c+1)N×(c+1)N$(c+1) N \times (c+1)
Sung‐Soo Byun, Seong‐Mi Seo, Meng Yang   +2 more
wiley   +1 more source

Poisson kernels of q$q$‐3D Hermite polynomials expansion for functions of several variables via generalized q$q$‐heat equations

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
wiley   +1 more source

Exceptional Differential Polynomial Systems Formed by Simple Pseudo-Wronskians of Jacobi Polynomials and Their Infinite and Finite X-Orthogonal Reductions

Mathematics
The paper advances a new technique for constructing the exceptional differential polynomial systems (X-DPSs) and their infinite and finite orthogonal subsets.
Gregory Natanson
doaj   +1 more source

A transference result of the $L^p$ continuity of the Jacobi Riesz transform to the Gaussian and Laguerre Riesz transforms [PDF]

, 2012
In this paper using the well known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials. We develop a transference method to obtain the $L^p$-continuity of the Gaussian-Riesz transform and the $L^p$-continuity of the ...
Eduard Navas, O. Urbina, Wilfredo
core  

Mehler-Heine asymptotics for multiple orthogonal polynomials

, 2016
Mehler-Heine asymptotics describe the behavior of orthogonal polynomials near the edges of the interval where the orthogonality measure is supported. For Jacobi polynomials and Laguerre polynomials this asymptotic behavior near the hard edge involves ...
Van Assche, Walter
core   +1 more source

Real models for the framed little n$n$‐disks operads

Journal of Topology, Volume 18, Issue 4, December 2025.
Abstract We study the action of the orthogonal group on the little n$n$‐disks operads. As an application we provide small models (over the reals) for the framed little n$n$‐disks operads. It follows in particular that the framed little n$n$‐disks operads are formal (over the reals) for n$n$ even and coformal for all n$n$.
Anton Khoroshkin, Thomas Willwacher
wiley   +1 more source

Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations

International Journal of Mathematics and Mathematical Sciences, 2011
We extend a collocation method for solving a nonlinear ordinary differential equation (ODE) via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in
Ahmad Imani, Azim Aminataei, Ali Imani
doaj   +1 more source

INTEGRAL REPRESENTATIONS FOR THE JACOBI–PINEIRO POLYNOMIALS AND THE FUNCTIONS OF THE SECOND KIND

Проблемы анализа, 2019
We consider the Hermite – Pad´e approximants for the Cauchy transforms of the Jacobi weights in one interval. The denominators of the approximants are known as Jacobi – Pi˜neiro polynomials.
V. G. Lysov
doaj   +1 more source

Using Reproducing Kernel for Solving a Class of Fractional Order Integral Differential Equations

Advances in Mathematical Physics, 2020
This paper is devoted to the numerical scheme for a class of fractional order integrodifferential equations by reproducing kernel interpolation collocation method with reproducing kernel function in the form of Jacobi polynomials.
Zhiyuan Li, Meichun Wang, Yulan Wang, Jing Pang   +3 more
doaj   +1 more source