Results 51 to 60 of about 906 (173)

A maple program to generate orthonormal polynomials

Computers & Mathematics with Applications, 1991
A Maple program for generating orthonormal polynomials with weight function \(w(x,k)=x^ k\) for even \(k\) is given. Numerical results are also presented.
openaire   +1 more source

Inequalities for orthonormal Laguerre polynomials

Journal of Approximation Theory, 2007
The following inequality is established: \[ 10^{-8}
openaire   +2 more sources

Representations of the Quantum Algebra su_q(1,1) and Discrete q-Ultraspherical Polynomials

Symmetry, Integrability and Geometry: Methods and Applications, 2005
We derive orthogonality relations for discrete q-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra su_q(1,1). Spectra and eigenfunctions of these operators are found explicitly.
Valentyna Groza
doaj  

A Cohen-Type Inequality for Jacobi-Sobolev Expansions

Journal of Inequalities and Applications, 2008
Let μ be the Jacobi measure supported on the interval [-1, 1]. Let us introduce the Sobolev-type inner product 〈f,g〉=∫−11f(x)g(x)dμ(x)+Mf(1)g(1)+Nf'(1)g'(1), where M,N≥0.
Bujar Xh. Fejzullahu
doaj   +1 more source

Orthogonal polynomials for exponential weights x2α(1 – x2)2ρe–2Q(x) on [0, 1)

Open Mathematics, 2020
Let Wα,ρ = xα(1 – x2)ρe–Q(x), where α > –12$\begin{array}{} \displaystyle \frac12 \end{array}$ and Q is continuous and increasing on [0, 1), with limit ∞ at 1.
Liu Rong
doaj   +1 more source

Spectral Representation and Simulation of Fractional Brownian Motion

Computation
This paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral
Konstantin Rybakov
doaj   +1 more source

Transverse Vibrations of Clamped and Simply-Supported Circular Plates with Two Dimensional Thickness Variation

Shock and Vibration, 2012
Two dimensional boundary characteristic orthonormal polynomials are used in the Ritz method for the vibration analysis of clamped and simply-supported circular plates of varying thickness. The thickness variation in the radial direction is linear whereas
N. Bhardwaj, A.P. Gupta, K.K. Choong, C.M. Wang, Hiroshi Ohmori   +4 more
doaj   +1 more source

On a two-dimensional analogue of the Lebesgue function for Fourier-Chebyshov sums [PDF]

E3S Web of Conferences
This article considers the problem of approximating a function of two variables f(x,y) by Fourier sums over Chebyshev polynomials orthogonal on a discrete grid.
Rustanov A.R., Shikhshinatova M.M.
doaj   +1 more source

The Approximate Integrals by the Reproducing Kernel Method on the Elliptical Region Eₙ In the Space Rⁿ [PDF]

مجلة جامعة النجاح للأبحاث العلوم الطبيعية
In this paper, we applied the reproducing kernel method on elliptical region, we establish the formulas of the reproducing kernel from several degrees and generalized those formulas whatever the dimension of space, we obtained all surfaces, points, and ...
Hiba Aslan, Hamed Abbas
doaj   +1 more source

FREE VIBRATION OF ISOTROPIC HALF-ELLIPTIC PLATES OF LINEARLY VARYING THICKNESS WITH CLAMPED CURVED BOUNDARY

International Islamic University Malaysia Engineering Journal, 2010
Two-dimensional boundary characteristic orthonormal polynomials are used in Rayleigh-Ritz method to study the title problem. In general, it is found that this method gives better results than the other traditional method such as boundary integral ...
A.P Gupta, N. Bhardwaj, K.K. Choong
doaj   +1 more source