Results 31 to 40 of about 75,283 (186)

A new approach in electromagnetic plane wave diffraction by two concentric slotted cylinders with variably placed slits: E and H polarized cases

IET Microwaves, Antennas &Propagation, Volume 16, Issue 7, Page 437-450, June 2022., 2022
Abstract The study investigates the electromagnetic plane wave diffraction by two concentric slotted cylinders with variably placed slits. Unlike the previous studies, the effect of rotation on the resonance characteristics and near‐field distributions is analyzed in the present work, which is not studied yet. The study focuses on diffraction by both E‐
Kamil Karaçuha, Vasil Tabatadze, Ömer Faruk Alperen, Eldar Veliev   +3 more
wiley   +1 more source

Ultraspherical/Gegenbauer polynomials to unify 2D/3D Ambisonic directivity designs [PDF]

arXiv
This report on axisymmetric ultraspherical/Gegenbauer polynomials and their use in Ambisonic directivity design in 2D and 3D presents an alternative mathematical formalism to what can be read in, e.g., my and Matthias Frank's book on Ambisonics or J\'er\^ome Daniel's thesis, Gary Elko's differential array book chapters, or Boaz Rafaely's spherical ...
Franz Zotter
openalex   +3 more sources

Weighted $$L^2$$-norms of Gegenbauer polynomials [PDF]

Aequationes mathematicae, 2022
We study integrals of the form \begin{equation*} \int_{-1}^1(C_n^{( )}(x))^2(1-x)^ (1+x)^ \, dx, \end{equation*} where $C_n^{( )}$ denotes the Gegenbauer-polynomial of index $ >0$ and $ , >-1$. We give exact formulas for the integrals and their generating functions, and obtain asymptotic formulas as $n\to\infty$.
Johann S. Brauchart, Peter J. Grabner
openaire   +2 more sources

Sequences of Non-Gegenbauer-Humbert Polynomials Meet the Generalized Gegenbauer-Humbert Polynomials [PDF]

ISRN Algebra, 2011
Here, we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known transfer formulas between non-Gegenbauer-Humbert polynomials and generalized Gegenbauer-Humbert polynomials are given.
Tian-Xiao He, Peter J.-S. Shiue
openaire   +2 more sources

On a generalization of the generating function for Gegenbauer polynomials [PDF]

Integral Transforms and Special Functions, 2013
A generalization of the generating function for Gegenbauer polynomials is introduced whose coefficients are given in terms of associated Legendre functions of the second kind. We discuss how our expansion represents a generalization of several previously derived formulae such as Heine's formula and Heine's reciprocal square-root identity.
openaire   +3 more sources

Mutually inverse series relating Ferrers and associated Legendre functions and generating functions pertaining to them [PDF]

arXiv, 2023
This article deals with three types of mutually inverse series relating Ferrers and associated Legendre functions of arbitrary complex indexes and orders established on the base of integral representations by using a number of generating functions (some of them are novel) for polynomials expressed in terms of hypergeometric or generalized ...
arxiv  

The Gegenbauer Polynomial Technique: the evaluation of a class of Feynman diagrams [PDF]

Phys.Lett. B375 (1996) 240-248, 1995
We extend Gegenbauer Polynomials technique to evaluate a class of complicated Feynman diagrams. New results in the form of $_3F_2$-hypergeometrical series of unit argument, are presented. As a by-product, we present a new transformation rule for $_3F_2$-hypergeometric series with argument $-1$.
arxiv   +1 more source

On the relation between Gegenbauer polynomials and the Ferrers function of the first kind [PDF]

arXiv, 2021
Using the direct relation between the Gegenbauer polynomials and the Ferrers function of the first kind, we compute interrelations between certain Jacobi polynomials, Meixner polynomials, and the Ferrers function of the first kind. We then compute Rodrigues-type and orthogonality relations for Ferrers functions of the first and second kinds.
arxiv  

The affine group and generalized Gegenbauer polynomials

Computers & Mathematics with Applications, 2001
AbstractOperators of the form f(xD) — g(L), where L is a shift (lowering) operator, arise naturally in the study of stochastic processes, such as Brownian motion, on the affine group. We find the polynomial eigenfunctions and the action of the affine group as well as the matrix elements of an exponential function corresponding to L.
Ph. Feinsilver, Uwe Franz
openaire   +2 more sources

Time‐Series Factor Modeling and Selection

Journal of Financial Research, EarlyView.
Abstract The article proposes a statistical time‐series factor model that incorporates deterministic orthogonal trend polynomials. Such polynomials allow capturing variation in returns without initially identifying a set of robust time‐series factors.
Michael Michaelides
wiley   +1 more source