Results 71 to 80 of about 1,811 (151)

Extremal weight enumerators and ultraspherical polynomials

Discrete Mathematics, 2003
The author establishes an upper bound for the minimum distance of a divisible code in terms of its dual distance, a result that generalizes the Mallows-Sloane bounds for self-dual codes. Moreover, there is a determination of zeta functions for the codes that attain this new bound.
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Differential Equations for Symmetric Generalized Ultraspherical Polynomials [PDF]

Transactions of the American Mathematical Society, 1994
We look for differential equations satisfied by the generalized Jacobi polynomials { P n α , β , M , N ( x ) } n = 0 ∞
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Multidomain spectral approach to rational‐order fractional derivatives

Studies in Applied Mathematics, Volume 152, Issue 4, Page 1110-1132, May 2024.
Abstract We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a multidomain approach; after transformations in accordance with the underlying Zq$Z_{q}$ curve ensuring ...
Christian Klein, Nikola Stoilov
wiley   +1 more source

On the Birkhoff Quadrature Formulas Using Even and Odd Order of Derivatives

Mathematical Problems in Engineering, Volume 2015, Issue 1, 2015., 2015
We introduce some New Quadrature Formulas by using Jacoby polynomials and Laguerre polynomials. These formulas can be obtained for a finite and infinite interval and also separately for the even or odd order of derivatives. By using the properties of error functions of the above orthogonal polynomials we can obtain the error functions for these ...
S. Hatami, S. M. Hashemiparast, S. Shateyi, Bing-Jean Lee   +3 more
wiley   +1 more source

A fast and well-conditioned spectral method for singular integral equations [PDF]

, 2016
We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems.
Olver, Sheehan, Slevinsky, Richard Mikael   +1 more
core   +1 more source

On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2006
The dual discrete $q$-ultraspherical polynomials $D_n^{(s)}(mu (x;s)|q)$ correspond to indeterminate moment problem and, therefore, have one-parameter family of extremal orthogonality relations.
Valentyna A. Groza, Ivan I. Kachuryk
doaj  

Asymptotic Properties of Derivatives of the Stieltjes Polynomials

Journal of Applied Mathematics, 2012
Let 𝑤𝜆(𝑥)∶=(1−𝑥2)𝜆−1/2 and 𝑃𝜆,𝑛(𝑥) be the ultraspherical polynomials with respect to 𝑤𝜆(𝑥). Then, we denote the Stieltjes polynomials with respect to 𝑤𝜆(𝑥) by 𝐸𝜆,𝑛+1(𝑥) satisfying ∫1−1𝑤𝜆(𝑥)𝑃𝜆,𝑛(𝑥)𝐸𝜆,𝑛+1(𝑥)𝑥𝑚𝑑𝑥=0, 0 ...
Hee Sun Jung, Ryozi Sakai
doaj   +1 more source

ONE-SIDED \(L\)-APPROXIMATION ON A SPHERE OF THE CHARACTERISTIC FUNCTION OF A LAYER

Ural Mathematical Journal, 2018
In the space \(L(\mathbb{S}^{m-1})\) of functions integrable on the unit sphere \(\mathbb{S}^{m-1}\) of the Euclidean space \(\mathbb{R}^{m}\) of dimension \(m\ge 3\), we discuss the problem of one-sided approximation to the characteristic function of a ...
Marina V. Deikalova, Anastasiya Yu. Torgashova   +1 more
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Legendre-Gauss-Lobatto grids and associated nested dyadic grids [PDF]

, 2013
Legendre-Gauss-Lobatto (LGL) grids play a pivotal role in nodal spectral methods for the numerical solution of partial differential equations. They not only provide efficient high-order quadrature rules, but give also rise to norm equivalences that could
Brix, Kolja, Canuto, Claudio, Dahmen, Wolfgang   +2 more
core   +1 more source

ON INTERPOLATION POLYNOMIALS USING THE ROOTS OF ULTRASPHERICAL POLYNOMIALS

Demonstratio Mathematica, 1984
Denote by \(x_ n,x_{n-1},...,x_ 1\) the roots of the ultraspherical polynomial \[ P_ n^{\alpha}(x)=(-1)^ n/(2^ nn!)(1-x^ 2)^{- \alpha}\frac{d^ n}{dx^ n}(1-x^ 2)^{n+\alpha}, \] where \(\alpha >- 1\) \((n=1,2,...)\) and consider the partition of [-1,1], \(\Delta ...
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