Results 41 to 50 of about 71,879 (309)
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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Linearization of the product of orthogonal polynomials of a discrete variable [PDF]
Applicationes Mathematicae, 1997 \textit{R. Askey} and \textit{G. Gasper} [J. Anal. Math. 31, 45-68 (1977; Zbl 0347.33006)] has given an explicit form for the coefficients in \(P_i(x)P_j(x)= \sum^{\min(i+j, B-1)}_{k= |i-j |} C_k^{ij} P_k(x)\), where \(\{P_k(x)\}\) be any system of classical orthogonal polynomials of a discrete variable. In this paper a linear recurrence relation for \(
Said Belmehdi +2 more
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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
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, 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 +8 more
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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 +4 more
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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 +3 more
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Solvable Discrete Quantum Mechanics: q-Orthogonal Polynomials with |q|=1 and Quantum Dilogarithm [PDF]
, 2015 Several kinds of q-orthogonal polynomials with |q|=1 are constructed as the main parts of the eigenfunctions of new solvable discrete quantum mechanical systems.
Gendenshtein L. E. +4 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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, 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 +16 more
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