Results 121 to 130 of about 180,252 (161)

A Bochner Theorem for Dunkl Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2011
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions.
Luc Vinet, Alexei Zhedanov
doaj   +1 more source

On the maximum value of Jacobi polynomials

Journal of Approximation Theory, 2005
A remarkable inequality with utterly explicit constants established by Erdélyi, Magnus and Nevai states that for \(\alpha\geq \beta> -{1\over 2}\) the orthonormal Jacobi polynomials \(P^{(\alpha,\beta)}_k\) satisfy \[ M(P^{(\alpha,\beta)}_k, \sqrt{1- x^2})= \max_{|x|\leq 1} \{(1- x)^{\alpha+{1\over 2}}(1+ x)^{\beta+{1\over 2}}(P^{(\alpha,\beta)}_k(x ...
openaire   +2 more sources

Darboux transformation of symmetric Jacobi matrices and Toda lattices

Frontiers in Applied Mathematics and Statistics
Let J be a symmetric Jacobi matrix associated with some Toda lattice. We find conditions for Jacobi matrix J to admit factorization J = LU (or J = 𝔘𝔏) with L (or 𝔏) and U (or 𝔘) being lower and upper triangular two-diagonal matrices, respectively.
Ivan Kovalyov, Oleksandra Levina
doaj   +1 more source

A numerical method based on the shifted Jacobi polynomials for a class of tempered fractional quadratic integro-differential equations

Results in Applied Mathematics
This paper introduces a new class of tempered fractional quadratic integro-differential equations using the Caputo fractional derivative. The existence and uniqueness of solutions to these equations are analyzed.
P. Senfiazad, M.H. Heydari, M. Bayram, D. Baleanu   +3 more
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The kernel polynomial method based on Jacobi polynomials

Applied Mathematics and Computation
The kernel polynomial method based on Jacobi polynomials $P_n^{α,β}(x)$ is proposed. The optimal-resolution positivity-preserving kernels and the corresponding damping factors are obtained. The results provide a generalization of the Jackson damping factors for arbitrary Jacobi polynomials.
I.O. Raikov, Y.M. Beltukov
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A short proof of a generating function for Jacobi polynomials

, 1980
A short proof is given for Bailey’s bilinear generating function for Jacobi polynomials. It depends only upon the orthogonality relation for Jacobi polynomials and a quadratic transformation for a hypergeometric series. A q-analog is also stated.
Dennis Stanton
core   +1 more source

From coin tossing to the jacobi polynomials

Journal of Combinatorial Theory, Series A, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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SRJAC: Sub-range Jacobi polynomials [version 1.0]

, 2014
Matlab routines for computing sub-range Jacobi polynomials within the sub interval of [-1 ...
Walter Gautschi,
core   +1 more source

Orthogonal polynomials Jacobi - Sobolev

, 2016
Este trabajo consiste en hacer un estudio de la teoría básica para comprender las tres primeras secciones del articulo "Polinomios ortogonales de Jacobi-Sobolev ".
Rios García, Nick Daniel
core  

On the Uniform Approximation of Smooth Functions by Jacobi Polynomials

, 1973
Let ωn(x) denote the Jacobi polynomials with the weight FunctionIf we denote the corresponding normalized Jacobi polynomials by we Have(1.1)Now letbe the nth partial sum of the Fourier series of Jacobi polynomials of a function f(x).
J. Prasad, H. Hayashi
core   +1 more source