Results 81 to 90 of about 6,433 (235)

Continuous −1$-1$ hypergeometric orthogonal polynomials

Studies in Applied Mathematics, Volume 153, Issue 3, October 2024.
Abstract The study of −1$-1$ orthogonal polynomials viewed as q→−1$q\rightarrow -1$ limits of the q$q$‐orthogonal polynomials is pursued. This paper presents the continuous polynomials part of the −1$-1$ analog of the q$q$‐Askey scheme. A compendium of the properties of all the continuous −1$-1$ hypergeometric polynomials and their connections is ...
Jonathan Pelletier, Luc Vinet, Alexei Zhedanov   +2 more
wiley   +1 more source

Matrix-valued Gegenbauer polynomials

, 2014
We introduce matrix-valued weight functions of arbitrary size, which are analogues of the weight function for the Gegenbauer or ultraspherical polynomials for the parameter $ >0$. The LDU-decomposition of the weight is explicitly given in terms of Gegenbauer polynomials. We establish a matrix-valued Pearson equation for these matrix weights leading
Koelink, Erik, Rios, Ana M. de los, Roman, Pablo   +2 more
openaire   +2 more sources

A note on the squarefree density of polynomials

Mathematika, Volume 70, Issue 4, October 2024.
Abstract The conjectured squarefree density of an integral polynomial P$\mathcal {P}$ in s$s$ variables is an Euler product SP$\mathfrak {S}_{\mathcal {P}}$ which can be considered as a product of local densities. We show that a necessary and sufficient condition for SP$\mathfrak {S}_{\mathcal {P}}$ to be 0 when P∈Z(X1,…,Xs)$\mathcal {P}\in \mathbb {Z}(
R. C. Vaughan, Yu. G. Zarhin
wiley   +1 more source

On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials

International Journal of Mathematics and Mathematical Sciences, 2007
We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer.
Stamatis Koumandos
doaj   +1 more source

Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds

Advances in Difference Equations, 2019
The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials.
Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, Dojin Kim   +3 more
doaj   +1 more source

Hermite and Gegenbauer polynomials in superspace using Clifford analysis

, 2007
The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way.
Bartocci C, Berezin F A, Brackx F, Brackx F, Cnops J, De Bie H, De Bie H, De Bie H, De Bie H Sommen F, De Bie H Sommen F, Delanghe R, F Sommen, Gilbert J E, H De Bie, Leites D A, Leites D A   +15 more
core   +2 more sources

Noise‐Tailored Constructions for Spin Wigner Function Kernels

Advanced Physics Research, Volume 3, Issue 6, June 2024.
This work explores the parameterization of spin Wigner functions to efficiently represent the effects of probabilistic unitary noise on a quantum state. Block diagonalization of the noise operator algebra is used to reduce the required number of parameters while maintaining the Stratonovich–Weyl conditions for the representation.
Michael Hanks, Soovin Lee, M.S. Kim
wiley   +1 more source

High-Order, Stable, And Efficient Pseudospectral Method Using Barycentric Gegenbauer Quadratures

, 2016
The work reported in this article presents a high-order, stable, and efficient Gegenbauer pseudospectral method to solve numerically a wide variety of mathematical models.
Elgindy, Kareem T.
core   +1 more source

A Non‐Standard Coupling Between Quantum Systems Originated From Their Kinetic Energy

Annalen der Physik, Volume 536, Issue 3, March 2024.
A novel approach to quantum coupling is introduced, departing from the conventional potential‐based interaction in standard quantum mechanics. Within this framework, a quantum coupling emerges from the inherent kinetic energy of particles. This unorthodox coupling results in the transformation of quantum mechanics' fundamental landscape through the ...
Tomer Shushi
wiley   +1 more source

A Convergent Legendre Spectral Collocation Method for the Variable‐Order Fractional‐Functional Optimal Control Problems

Journal of Mathematics, Volume 2024, Issue 1, 2024.
In this paper, a numerical method is applied to approximate the solution of variable‐order fractional‐functional optimal control problems. The variable‐order fractional derivative is described in the type III Caputo sense. The technique of approximating the optimal solution of the problem using Lagrange interpolating polynomials is employed by ...
Zahra Pirouzeh, Mohammad Hadi Noori Skandari, Kameleh Nassiri Pirbazari, Ammar Alsinai   +3 more
wiley   +1 more source