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Classical and generalized Jacobi polynomials orthogonal with different weight functions and differential equations satisfied by these polynomials [PDF]

, 2017
summary:In this contribution we deal with classical Jacobi polynomials orthogonal with respect to different weight functions, their special cases - classical Legendre polynomials and generalized brothers of them.
Marčoková, Mariana, Guldan, Vladimír
core   +1 more source

Jacobi Polynomial Expansions

Journal of Mathematical Analysis and Applications, 1994
The paper is devoted to eigenfunction expansions associated with Jacobi polynomials \([^{\alpha,\beta} P_ n]^ \infty_{n=0}\). The classical expansion associated with the Jacobi operator is well-known when \(a>-1\), \(\beta> -1\). It is shown that when \(\alpha\), \(\beta-1\).
openaire   +2 more sources

Optimal Gain Selection for the Arbitrary‐Order Homogeneous Differentiator

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Differentiation of noisy signals is a relevant and challenging task. Widespread approaches are the linear high‐gain observer acting as a differentiator and Levant's robust exact differentiator with a discontinuous right‐hand side. We consider the family of arbitrary‐order homogeneous differentiators, which includes these special cases.
Benjamin Calmbach, Jaime A. Moreno, Johann Reger   +2 more
wiley   +1 more source

On the Integral Representation of Jacobi Polynomials

Mathematics
In this paper, we present a new integral representation for the Jacobi polynomials that follows from Koornwinder’s representation by introducing a suitable new form of Euler’s formula.
Enrico De Micheli
doaj   +1 more source

Validation of Neural Network Controllers for Uncertain Systems Using the Keep‐Close Approach: Robustness Analysis and Safety Verification

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT The safety verification of neural network (NN) controllers operating in uncertain environments characterized by unmodeled dynamics, nonlinearities, and time delays remains a fundamental challenge in robust control analysis. This article introduces a novel method, termed Keep‐Close, for analyzing the performance and robustness of uncertain ...
Abdelhafid Zenati, Nabil Aouf
wiley   +1 more source

Polynomial‐shaped electrodes for adaptive X‐ray optics

Journal of Synchrotron Radiation, EarlyView.
A shaped electrode design for lithium niobate adaptive X‐ray mirrors connects actuator degrees of freedom to specific polynomial orders, enabling general shape control and the correction of defocus, coma and fourth‐order aberrations with a limited number of inputs.For adaptive mirrors on X‐ray beamlines and optical systems, we describe a strategy for ...
Kenneth A. Goldberg, Francesco Marzari, Grant D. Cutler   +2 more
wiley   +1 more source

Establishing Shape Correspondences: A Survey

Computer Graphics Forum, EarlyView.
Abstract Shape correspondence between surfaces in 3D is a central problem in geometry processing, concerned with establishing meaningful relations between surfaces. While all correspondence problems share this goal, specific formulations can differ significantly: Downstream applications require certain properties that correspondences must satisfy ...
A. Heuschling, H. Meinhold, L. Kobbelt
wiley   +1 more source

Recurrence Relations for Jacobi Orthogonal Polynomials on the Triangular Domain

Image Analysis and Stereology
In this paper, we present recurrence relations for the Jacobi weighted orthogonal polynomials Pn,r(α,β,γ) (u, v, w) with r = 0, 1, . . . , n, where n ≥ 0, defined on the triangular domain T = {(u, v, w) : u, v, w ≥ 0, u + v + w = 1} for values of α, β ...
Wala’a A. AlKasasbeh, Abedallah Rababah, Iqbal Batiha, Iqbal H. Jebril, Hamzah O. Al-Khawaldeh, Radwan M. Batyha   +5 more
doaj   +1 more source

Extended Jacobi Functions via Riemann-Liouville Fractional Derivative

Abstract and Applied Analysis, 2013
By means of the Riemann-Liouville fractional calculus, extended Jacobi functions are de…fined and some of their properties are obtained. Then, we compare some properties of the extended Jacobi functions extended Jacobi polynomials.
Bayram Çekim, Esra Erkuş-Duman
doaj   +1 more source

Representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials

Journal of Inequalities and Applications, 2017
A representation of ( p , q ) $(p,q)$ -Bernstein polynomials in terms of ( p , q ) $(p,q)$ -Jacobi polynomials is obtained.
F Soleyman, I Area, M Masjed-Jamei, JJ Nieto   +3 more
doaj   +1 more source