Results 41 to 50 of about 263,554 (202)
On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2
International Journal of Mathematics and Mathematical Sciences, 2009 Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2.
Tian-Xiao He, Peter J.-S. Shiue
doaj +1 more source
Advances in Difference Equations, 2019 The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials.
Taekyun Kim +3 more
doaj +1 more source
Detecting Periodicity of a General Stationary Time Series via AR(2)‐Model Fitting
Journal of Time Series Analysis, EarlyView.ABSTRACT Estimating the periodicity of a stationary time series via fitting a second‐order stationary autoregressive (AR(2)) model has been initiated by the seminal paper of Yule (1927). We investigate properties of this procedure when applied to general stationary processes possessing a spectral density with a dominant peak at some unknown frequency ...
Jens‐Peter Kreiss +2 more
wiley +1 more source
Probing Strong Coupling in Core–Shell Nanoparticles With Fast Electron Beams
physica status solidi (a), Volume 223, Issue 17, 9 September 2026.An exact analytic formalism for evaluating electron‐energy loss and cathodoluminescence probabilities for core–shell nanoparticles explored by electron‐beam spectroscopies is derived. The formalism is exploited to understand strong exciton–plasmon and exciton–Mie mode coupling in nanophotonic architectures.
Annika Brandt +3 more
wiley +1 more source
Approximation and Orthogonality on Fully Symmetric Domains
Studies in Applied Mathematics, Volume 156, Issue 1, January 2026.ABSTRACT We study orthogonal polynomials on a fully symmetric planar domain Ω$\Omega$ that is generated by a certain triangle in the first quadrant. For a family of weight functions on Ω$\Omega$, we show that orthogonal polynomials that are even in the second variable on Ω$\Omega$ can be identified with orthogonal polynomials on the unit disk composed ...
Yuan Xu
wiley +1 more source
A Quadruple Integral Containing the Gegenbauer Polynomial Cn(λ)(x): Derivation and Evaluation
, 2022 A four-dimensional integral containing g(x,y,z,t)Cn(λ)(x) is derived. Cn(λ)(x) is the Gegenbauer polynomial, g(x,y,z,t) is a product of the generalized logarithm quotient functions and the integral is taken over the region 0≤x≤1,0&le ...
Robert Reynolds, Allan Stauffer
core +1 more source
MathematicsThis paper introduces a novel hybrid shifted Gegenbauer integral–pseudospectral (HSG-IPS) method to solve the time-fractional Benjamin–Bona–Mahony–Burgers (FBBMB) equation with high accuracy.
Kareem T. Elgindy
doaj +1 more source
Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.In this study, we introduce the two‐parameter Pochhammer matrix function. Notably, we establish the (p, k) Pochhammer matrix symbol as a key new construct for our generalizations. Furthermore, we construct gamma and beta matrix functions of two parameters and prove properties similar to their classical counterparts.
Mohamed S. Al–Sheikh +4 more
wiley +1 more source
A Review of Certain Modern Special Functions and Their Applications
Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions.
Hala Abd Elmageed +2 more
wiley +1 more source
Gegenbauer type polynomial solutions for the higher spin laplace operator
, 2016 : In this paper we study special polynomial solutions to the higher spin Laplace operator, which is a conformally invariant second-order operator acting on fields taking values in the space of symmetric tensors.
David Eelbode +3 more
core +1 more source