Results 61 to 70 of about 139,435 (183)

Block orthogonal polynomials: I. Definition and properties

, 2007
Constrained orthogonal polynomials have been recently introduced in the study of the Hohenberg-Kohn functional to provide basis functions satisfying particle number conservation for an expansion of the particle density.
Abramowitz M, Andrews G E, Bateman H, Bourbaki N, Chihara T S, Dieudonné J, Dreizler R M, Fiolhais C, Giraud B G, Gradshteyn I S, Halmos P R, Jean-Marie Normand, Kreyszig E, Lang S, Mehta M L, Messiah A, Normand J-M, Szegö G   +17 more
core   +4 more sources

BESSEL POLYNOMIALS AND SOME CONNECTION FORMULAS IN TERMS OF THE ACTION OF LINEAR DIFFERENTIAL OPERATORS

Ural Mathematical Journal, 2022
In this paper, we introduce the concept of the \(\mathbb{B}_{\alpha}\)-classical orthogonal polynomials, where \(\mathbb{B}_{\alpha}\) is the raising operator \(\mathbb{B}_{\alpha}:=x^2 \cdot {d}/{dx}+\big(2(\alpha-1)x+1\big)\mathbb{I}\), with nonzero ...
Baghdadi Aloui, Jihad Souissi
doaj   +1 more source

Characterization of the generalized Chebyshev-type polynomials of first kind

, 2015
Orthogonal polynomials have very useful properties in the solution of mathematical problems, so recent years have seen a great deal in the field of approximation theory using orthogonal polynomials.
AlQudah, Mohammad A.
core   +2 more sources

On 2-orthogonal polynomials of Laguerre type

International Journal of Mathematics and Mathematical Sciences, 1999
Let {Pn}n≥0 be a sequence of 2-orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let {Qn}n≥0 be the sequence of polynomials defined by Qn:=(n+1)−1P′n+1,n≥0.
Khalfa Douak
doaj   +1 more source

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

, 1993
Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis ...
A Pringsheim, A Pringsheim, A Seiberg, AA Gonchar, AA Markov, AA Markov, AA Markov, AM Al-Rashed, AS Kronrod, AS Kronrod, B Baillaud, C Berg, C Brezinski, C Hermite, CL Siegel, D Hubert, D Hubert, D Hubert, DS Lubinsky, DV Chudnovsky, DV Chudnovsky, E Cosserat, E Hendriksen, EB Christoffel, EB Vleck Van, EB Vleck Van, EB Vleck Van, F Hausdorff, F Peherstorfer, FWJ Olver, G Darboux, G Darboux, G Freud, G Gasper, G Monegato, G Polya, G Szegö, G Szegö, G Szegő, G Vitali, G Vitali, GH Hardy, GH Hardy, H Bruns, H Hamburger, H Hamburger, H Hamburger, H Padé, H Padé, H Stahl, H Widom, H Widom, H Zaheer, HN Mhaskar, HS Wall, J Favard, JA Shohat, JA Shohat, JL Ullman, K Aomoto, K Possé, K Possé, L Carlitz, L Lorch, L Lorentzen, L Schur, LJ Rogers, LJ Rogers, M Alam, M Fekete, M Prévost, M Riesz, M Tsuji, MEH Ismail, MEH Ismail, MG Krein, MG Krein, MH Stone, ML Mehta, NI Akhiezer, NY Vilenkin, O Njåstad, O Perron, O Perron, P Erdős, P Montel, PG Nevai, PJ Forrester, PL Chebyshev, PL Pastro, R Askey, RA Gustafson, S Karlin, S Karlin, S Karlin, T Carleman, T Carleman, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TJ Stieltjes, TS Chihara, TS Chihara, TS Chihara, W Assche Van, W Gautschi, W Gautschi, W Gautschi, W Hahn, W Ledermann, WB Jones, WB Jones, WB Jones, YL Geronimus   +121 more
core   +2 more sources

Szegő polynomials: some relations to L-orthogonal and orthogonal polynomials

Journal of Computational and Applied Mathematics, 2003
The authors consider the Szegö polynomials \(S_n(z)\) with real reflection coefficients and obtain some relations to certain self-inverse orthogonal \(L\)-polynomials defined on the unit circle and corresponding symmetric orthogonal polynomials on a real line. The polynomials obtained by rotating the coefficients in the recursive relations satisfied by
Bracciali, Cleonice Fátima, da Silva, A. P., Ranga, A. S.   +2 more
openaire   +4 more sources

Recurrence Relations for Orthogonal Polynomials on Triangular Domains

Mathematics, 2016
In Farouki et al, 2003, Legendre-weighted orthogonal polynomials P n , r ( u , v , w ) , r = 0 , 1 , … , n , n ≥ 0 on the triangular domain T = { ( u , v , w ) : u , v , w ≥ 0 , u + v + w = 1 } are constructed, where u , v , w
Abedallah Rababah
doaj   +1 more source

Solving change of basis from Bernstein to Chebyshev polynomials

Examples and Counterexamples
We provide two closed-form solutions to the change of basis from Bernstein polynomials to shifted Chebyshev polynomials of the fourth kind and show them to be equivalent by applying Zeilberger’s algorithm. The first solution uses orthogonality properties
D.A. Wolfram
doaj   +1 more source

Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach

, 2002
We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal polynomials; b ...
Andreev, Balantekin, Basor, Bleher, Brézin, Brézin, Deift, Deift, Deift, Deift, Eugene Strahov, Fokas, Fokas, Forrester, Forrester, Fyodorov, Fyodorov, Fyodorov, Fyodorov, Fyodorov, Fyodorov, Fyodorov, Fyodorov, Gonek, Hughes, Hughes, Its, Johansson, Kanzieper, Keating, Mehta, Mirlin, Nonnenmacher, Splittorff, Tracy, Tracy, Tracy, Yan V. Fyodorov   +37 more
core   +1 more source

Studies on the Method of Orthogonal Collocation III. The Use of Jacobi Orthogonal Polynomials for the Solution of Boundary Value Problems

Journal of King Saud University: Engineering Sciences, 1999
Previous work identified the kind of Jocobi polynomials suitable to solve boundary value problems of the diffusion type in a slab, cylinder or sphere.
Mostafa Ali Soliman, A.A. Ibrahim
doaj   +1 more source