Results 71 to 80 of about 3,034 (119)

An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials

Advances in Applied Mathematics, 2002
In this interesting paper the author studies generalized Gegenbauer polynomials that are orthogonal with respect to the weight function \(|x|^{2\mu}\) \((1-x^2)^{\lambda- {1\over 2}}\). First, an important integral formula is established for these polynomials that serves as a transformation between \(h\)-harmonics of different parameters and contains ...
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Certain theorems on bilateral generating functions involving Hermite, Laguerre, and Gegenbauer polynomials

Journal of Mathematical Analysis and Applications, 1990
The object of this paper is to present simpler proofs of the various generalizations of some interesting results on bilateral generating functions which were derived recently by \textit{P. N. Shrivastava} and \textit{B. Kaur} [J. Indian. Math. Soc., New Ser. 49(1987), 179-183 (1985; Zbl 0642.33022)] using group-theoretic methods.
Hubbell, John H, Srivastava, H.M
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Gegenbauer polynomials for certain subclasses of Bazilevic functions associated with a generalized operator defined by convolution

Gulf Journal of Mathematics, 2023
In this paper, a class Gη_1,η_2β(α,t), consisting of Bazilevic functions of type α and involving a certain generalized differential operator is defined by means of Gegenbauer polynomials. Initial coefficient bounds and Fekete-Szego estimates for functions belonging to this class are obtained.
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Radon Transform on spheres and generalized Bessel function associated with dihedral groups [PDF]

, 2012
Motivated by Dunkl operators theory, we consider a generating series involving a modified Bessel function and a Gegenbauer polynomial, that generalizes a known series already considered by L. Gegenbauer. We actually use inversion formulas for Fourier and
Demni, Nizar
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Two-dimensional unsteady waves in an electromagnetoelastic sphere

Учёные записки Казанского университета: Серия Физико-математические науки, 2017
The propagation of unsteady kinematic or electromagnetic perturbations in an isotropic ball given on its surface has been studied. Along with the Maxwell equations and the linearized Ohm's law, we have studied the linear equations of motion for an ...
V.A. Vestyak, D.V. Tarlakovskii
doaj  

Almost everywhere convergence of orthogonal expansions of several variables

, 2003
For weighted $L^1$ space on the unit sphere of $\RR^{d+1}$, in which the weight functions are invariant under finite reflection groups, a maximal function is introduced and used to prove the almost everywhere convergence of orthogonal expansions in $h ...
Xu, Yuan
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Analytical Solution of Generalized Fractional Integro-Differential Equations via Shifted Gegenbauer Polynomials

MATEMATIKA
In this paper, we proposed an analytical solution for generalized fractional order integro-differential equations with non-local boundary conditions via shifted Gegenbauer polynomials as an approximating polynomial using the Galerkin method and collocation techniques involving operational matrix that make use of the Liouville-Caputo operator of ...
Kazeem Issa, Adebayo Ridwan, Muritala Hambali Suleiman   +2 more
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On a generalized class of \(q\)-Gegenbauer polynomials and subordination-defined bi-univalent functions

Open Journal of Mathematical Analysis
This work introduces a unique family of bi-univalent functions utilising \(q\)-Gegenbauer polynomials. The estimates of the initial coefficients \(\left\vert a_{2}\right\vert\) and \(\left\vert a_{2}\right\vert\) for functions in this new class, together with the Fekete-Szegö functional, have been obtained.
Abdullah Alatawi, Sarem H Hadi, Youssef T. Laz   +2 more
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On the asymptotic behavior of the maximum absolute value of generalized Gegenbauer polynomials

, 2016
Using well-known facts on Jacobi polynomials, we derive some asymptotic estimates for the maximum absolute value of generalized Gegenbauer polynomials.
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The weight functions, generating functions and miscellaneous properties of the sequences of orthogonal polynomials of the second kind associated with the Jacobi and the Gegenbauer polynomials

Journal of Computational and Applied Mathematics, 1986
The main object of the paper is the calculation and study of the weight functions and orthogonality relations corresponding to sequences of polynomials of the second kind associated with the Jacobi and the Gegenbauer polynomials. Section 2 contains the underlying theory restricted to the citation of a few general formulas regarding the orthogonality of
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