Results 51 to 60 of about 75,283 (186)
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this paper, a numerical method is applied to approximate the solution of variable‐order fractional‐functional optimal control problems. The variable‐order fractional derivative is described in the type III Caputo sense. The technique of approximating the optimal solution of the problem using Lagrange interpolating polynomials is employed by ...
Zahra Pirouzeh +3 more
wiley +1 more source
Initial Coefficient Estimates for Bi‐Univalent Functions Related to Generalized Telephone Numbers
Journal of Mathematics, Volume 2024, Issue 1, 2024.This study defines three novel classes of bi‐univalent functions connected to generalized telephone numbers for the first time. We produced assessments about the Taylor–Maclaurin coefficients |a2| and |a3| and Fekete–Szegö functional problems for functions involving these novel subclasses for functions in every one regarding these three bi‐univalent ...
Gangadharan Murugusundaramoorthy +5 more
wiley +1 more source
Mixed-Type Hypergeometric Bernoulli–Gegenbauer Polynomials
Mathematics, 2023 In this paper, we consider a novel family of the mixed-type hypergeometric Bernoulli–Gegenbauer polynomials. This family represents a fascinating fusion between two distinct categories of special functions: hypergeometric Bernoulli polynomials and Gegenbauer polynomials. We focus our attention on some algebraic and differential properties of this class
Dionisio Peralta +2 more
openaire +2 more sources
Double Gegenbauer expansion of $|s - t|^α$ [PDF]
Integral Transform and Special Functions, 2019, 2019 We give a Gegenbauer expansion of the two variable function $| s - t |^{\alpha}$ in terms of the ultraspherical polynomials $C_l^{\lambda} (s)$ and $C^{\mu}_m (t)$. Generalization, specialization, and limits of the expansion are also discussed.
arxiv +1 more source
Random Gegenbauer Features for Scalable Kernel Methods [PDF]
arXiv, 2022 We propose efficient random features for approximating a new and rich class of kernel functions that we refer to as Generalized Zonal Kernels (GZK). Our proposed GZK family, generalizes the zonal kernels (i.e., dot-product kernels on the unit sphere) by introducing radial factors in their Gegenbauer series expansion, and includes a wide range of ...
arxiv
An application of Gegenbauer polynomials in queueing theory
Journal of Computational and Applied Mathematics, 1993 AbstractThe symmetric coupled processor model is a queueing system in which a server divides his service capacity between two independent streams of customers, unless one queue is empty, in which case the full capacity is granted to the other queue.
Ellen De Waard +2 more
openaire +2 more sources
On Exponential Convergence of Gegenbauer Interpolation and Spectral Differentiation [PDF]
arXiv, 2011 This paper is devoted to a rigorous analysis of exponential convergence of polynomial interpolation and spectral differentiation based on the Gegenbauer-Gauss and Gegenbauer-Gauss-Lobatto points, when the underlying function is analytic on and within an ellipse. Sharp error estimates in the maximum norm are derived.
arxiv
Generalizations and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals [PDF]
arXiv, 2012 In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer polynomials through extension a two element sequence of generating functions for Jacobi polynomials.
arxiv
The Gegenbauer polynomials and typically real functions
Journal of Computational and Applied Mathematics, 2003 AbstractLinear and nonlinear coefficient problems for some class of typically real functions are studied. Different inequalities for the Gegenbauer polynomials appear to be very useful.
K. Kiepiela, I. Naraniecka, Jan Szynal
openaire +2 more sources
Application of a composition of generating functions for obtaining explicit formulas of polynomials [PDF]
arXiv, 2012 Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Laguerre polynomials, Stirling polynomials, Abel polynomials, Bernoulli Polynomials of the Second Kind, Generalized Bernoulli polynomials, Euler Polynomials, Peters ...
arxiv