Results 71 to 80 of about 73,008 (249)

Orthogonal Basic Hypergeometric Laurent Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2012
The Askey-Wilson polynomials are orthogonal polynomials in$x = cos heta$, which are given as a terminating $_4phi_3$ basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in $z=e^{iheta}$, which are given as a ...
Mourad E.H. Ismail, Dennis Stanton
doaj   +1 more source

Discrete and Differential Equations in Applied Mathematics

Communications, 2008
In the contribution we map investigations performed in mathematics at the Faculty of Science in 2003-2007. Main directions developed at the faculty are described and some of the latest achievements are presented.
Miroslava Ruzickova
doaj   +1 more source

Multiple Meixner Polynomials on a Non-Uniform Lattice

Mathematics, 2020
We consider two families of type II multiple orthogonal polynomials. Each family has orthogonality conditions with respect to a discrete vector measure.
Jorge Arvesú, Andys M. Ramírez-Aberasturis   +1 more
doaj   +1 more source

Dual -1 Hahn polynomials: "classical" polynomials beyond the Leonard duality [PDF]

, 2011
We introduce the -1 dual Hahn polynomials through an appropriate $q \to -1$ limit of the dual q-Hahn polynomials. These polynomials are orthogonal on a finite set of discrete points on the real axis, but in contrast to the classical orthogonal ...
Tsujimoto, Satoshi, Vinet, Luc, Zhedanov, Alexei   +2 more
core  

Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm

, 2011
The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adjacency, which amounts to the inclusion of shifted weight functions in the ...
Bareiss E H, Bressoud D, Brezinski C, Brezinski C, Brezinski C, Brezinski C, Chihara T S, Draux A, Erdelyi A, Frank W Nijhoff, Henrici P, Kowalewski G, Krichever I M, Krichever I M, Lomont J S, Malaschonok G I, Malaschonok G I, Muir T, Paul E Spicer, Peter H van der Kamp, Spicer P E, Suetin P K, Toda M, van der Kamp P H, van der Kamp P H, Veselov A P, Viallet C   +26 more
core   +1 more source

Discrete Orthogonal Polynomials with Hypergeometric Weights and Painlevé VI [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2018
We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-negative integers with hypergeometric weights and show that they satisfy a system of non-linear difference equations and a non-linear second order differential equation in one of the parameters of the weights.
Van Assche, Walter, Filipuk, Galina
openaire   +4 more sources

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

APPROXIMATIVE PROPERTIES OF FOURIER-MEIXNER SUMS

Проблемы анализа, 2018
We consider the problem of approximation of discrete functions f = f(x) defined on the set Ω_δ = {0, δ, 2δ, . . .}, where δ =1/N, N > 0, using the Fourier sums in the modified Meixner polynomials M_(α;n,N)(x) = M(α;n)(Nx) (n = 0, 1, . . .), which for α >
Gadzhimirzaev R. M.
doaj   +1 more source

Semi-classical Laguerre polynomials and a third order discrete integrable equation

, 2009
A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specific semi-classical orthogonal polynomial weight. The main example we use is
Christoffel E B, Darboux G, Forrester P J Witte N S, Forrester P J Witte N S, Frank W Nijhoff, Freud G, Grammaticos B, Laguerre E, Laguerre E, Laguerre E, Lax P D, Magnus A P, Paul E Spicer   +12 more
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On Generating Orthogonal Polynomials for Discrete Measures

Zeitschrift für Analysis und ihre Anwendungen, 1998
In the present paper, we derive an algorithm for computing the recurrence coefficients of orthogonal polynomials with respect to discrete measures. This means that the support of the measure is a finite set. The algorithm is based oniormulae of Nevai describing the transformation of recurrence coefficients, if we add a point mass to the measure of ...
openaire   +3 more sources