Results 31 to 40 of about 2,361 (229)

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 \(\alpha\), \(\beta-1\).
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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

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

Iterated Integrals of Jacobi Polynomials [PDF]

Bulletin of the Malaysian Mathematical Sciences Society, 2019
Let P(α,β)n be the n-th monic Jacobi polynomial with α,β>−1. Given m numbers ω1,…,ωm∈C∖[−1,1], let Ωm=(ω1,…,ωm) and P(α,β)n,m,Ωm be the m-th iterated integral of (n+m)!n!P(α,β)n normalized by the conditions dkP(α,β)n,m,Ωmdzk(ωm−k)=0, for k=0,1,…,m−1. The main purpose of the paper is to study the algebraic and asymptotic properties of the sequence of ...
Hector Pijeira-Cabrera, Daniel Rivero-Castillo   +1 more
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Generating functions for the Jacobi polynomial [PDF]

Proceedings of the American Mathematical Society, 1976
Two theorems are proved with the aid of operator and series iteration methods. Special cases appear to give new and known generating functions for the Jacobi polynomial.
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A priori estimates and large population limits for some nonsymmetric Nash systems with semimonotonicity

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We address the problem of regularity of solutions ui(t,x1,…,xN)$u^i(t, x^1, \ldots, x^N)$ to a family of semilinear parabolic systems of N$N$ equations, which describe closed‐loop equilibria of some N$N$‐player differential games with Lagrangian having quadratic behaviour in the velocity variable, running costs fi(x)$f^i(x)$ and final costs gi(
Marco Cirant, Davide Francesco Redaelli
wiley   +1 more source

A Transference Result of the Lp-Continuity of the Jacobi Littlewood-Paley g-Function to the Gaussian and Laguerre Littlewood-Paley g-Function

Journal of Function Spaces, 2018
We develop a transference method to obtain the Lp-continuity of the Gaussian-Littlewood-Paley g-function and the Lp-continuity of the Laguerre-Littlewood-Paley g-function from the Lp-continuity of the Jacobi-Littlewood-Paley g-function, in dimension one,
Eduard Navas, Wilfredo O. Urbina
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Uncertainty Quantification for Nonlinear Vibration of Supercritical Drive Shaft With a Dry Friction Damper

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT The supercritical drive shaft is becoming increasingly popular in helicopter transmission system. Dry friction dampers are specially employed to ensure the supercritical shafts crossing the critical speed safely. Due to design tolerances, manufacturing errors and time‐varying factors, the parameters of the damper are inherently uncertain ...
Liyao Song, Meijun Liao, Weifang Chen, Rupeng Zhu, Dan Wang   +4 more
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
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A Physics‐Informed Learning Framework to Solve the Infinite‐Horizon Optimal Control Problem

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT We propose a physics‐informed neural networks (PINNs) framework to solve the infinite‐horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations (PDEs), they can be employed to learn the value function of the infinite‐horizon optimal control problem via
Filippos Fotiadis, Kyriakos G. Vamvoudakis   +1 more
wiley   +1 more source