Results 51 to 60 of about 133,676 (303)

A Probablistic Origin for a New Class of Bivariate Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2008
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an ...
Michael R. Hoare, Mizan Rahman
doaj   +1 more source

Orthogonal Polynomials in Mathematical Physics

, 2017
This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory.
Chan, Chuan-Tsung, Mironov, A., Morozov, A., Sleptsov, A.   +3 more
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Discrete Fourier Analysis and Chebyshev Polynomials with $G_2$ Group [PDF]

, 2012
The discrete Fourier analysis on the $30^{\degree}$-$60^{\degree}$-$90^{\degree}$ triangle is deduced from the corresponding results on the regular hexagon by considering functions invariant under the group $G_2$, which leads to the definition of four ...
Li, Huiyuan, Sun, Jiachang, Xu, Yuan
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Discrete semi-classical orthogonal polynomials: generalized Charlier

Journal of Computational and Applied Mathematics, 2000
Charlier polynomials are discrete orthogonal polynomials on the integers with respect to the Poisson distribution, i.e., with weights \(\mu^k/k!\) at the points \(k \in {\mathbb N}\). The generalized Charlier polynomials in this paper are discrete orthogonal polynomials with weights \(\mu^k/(k!)^r\).
Hounkonnou, M., Hounga, C., Ronveaux, André   +2 more
openaire   +2 more sources

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

IEEE Access, 2023
Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials and used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision.
Basheera M. Mahmmod, Sadiq H. Abdulhussain, Tomas Suk, Muntadher Alsabah, Abir Hussain   +4 more
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Generalized squeezed-coherent states of the finite one-dimensional oscillator and matrix multi-orthogonality

, 2012
A set of generalized squeezed-coherent states for the finite u(2) oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes determined by matrix elements of exponentials in the su(2) generators.
Alexei Zhedanov, Atakishiyev N M, Luc Vinet, Niederer U, Niederer U, Vincent X Genest, Vinet L, Wang X, Wigner E P   +8 more
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Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems

Symmetry, Integrability and Geometry: Methods and Applications, 2012
Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (
Hiroshi Miki, Hiroaki Goda, Satoshi Tsujimoto   +2 more
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A hidden analytic structure of the Rabi model

, 2013
The Rabi model describes the simplest interaction between a cavity mode with a frequency $\omega_c$ and a two-level system with a resonance frequency $\omega_0$.
Moroz, Alexander
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Stable Calculation of Krawtchouk Functions from Triplet Relations

Mathematics, 2021
Deployment of the recurrence relation or difference equation to generate discrete classical orthogonal polynomials is vulnerable to error propagation. This issue is addressed for the case of Krawtchouk functions, i.e., the orthonormal basis derived from ...
Albertus C. den Brinker
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LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials

, 2006
For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q=0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations.
A. Okounkov, C. Krattenthaler, C.F. Dunkl, H.T. Koelink, I.G. Macdonald, K.T. Andrews, K.T. Andrews, L. Carlitz, M. Voit, P. Terwilliger, P. Terwilliger, P. Terwilliger, T.H. Koornwinder, Tom H. Koornwinder, U. Onn, Uri Onn, W. Groenevelt   +16 more
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