The Bessel-Muirhead hypergeometric system (or 0 F 1-system) in two variables (and three variables) is solved using symmetric series, with an explicit formula for coefficients , in order to express the K-Bessel function as a linear combination of the J-solutions. Limits of this method and suggestions for generalizations to a higher rank are discussed. 1. Introduction. The Bessel functions (of th...

Keywords: Squared spherical Bessel functions Regularization of Hankel series Gaussian power-law densities Kummer distributions Airy approximation of Bessel integrals a b s t r a c t Bessel integrals of type R 1 0 k lþ2 e Àak 2 ÀðbþixÞk j 2 l ðpkÞdk are studied, where the squared spherical Bessel function j 2 l is averaged with a modulated Gaussian power-law density. These inte-grals define the ...

An approach of generating broadband Bessel beams is presented. The broadband Bessel beams are produced by a gradient index (GRIN) metamaterial lens illuminated by broadband waveguide antenna. The metamaterial lens is constructed with multi-layered structure and each layer is composed of GRIN metamaterials. The metamaterials are designed as dielectric plates printed with metallic patterns in the...

The scintillation index is formulated for modified Bessel-Gaussian beams propagating in weakly turbulent media. Numerical calculations applied directly to the derived triple integral show that, for off-axis positions, the modified Bessel-Gaussian beams of higher than zero order scintillate less than Gaussian beams at large input beam sizes and low beam orders with the increasing width parameter...

Abstra t: In the early 1950's, Emil Grosswald began investigating the irredu ibility of the Bessel polynomials yn(x) and onje tured the irredu ibility of yn(x) over the rationals for all positive integers n. This paper resolves the onje ture by establishing the irredu ibility of a lass of polynomials that in ludes the Bessel polynomials.

We find the high energy asymptotics for the singular Weyl–Titchmarsh m-functions and the associated spectral measures of perturbed spherical Schrödinger operators (also known as Bessel operators). We apply this result to establish an improved local Borg–Marchenko theorem for Bessel operators as well as uniqueness theorems for the radial quantum scattering problem with nontrivial angular momentum.

We investigate the ultraslow motion of polychromatic Bessel beams in unbounded, nondispersive media. Control over the group velocity is exercised by means of the angular dispersion of pulsed Bessel beams of invariant transverse spatial frequency, which spontaneously emerge from near-field generators. Temporal dynamics in transients and resonances over homogeneous delay lines (dielectric slabs) ...

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

Bessel functions of matrix argument appeared as a subject of studies in the work of Herz [6]. One can find in the multivariate statistics literature some applications of these functions (see [11]). The main tool of Herz’s work was the Laplace transform and its inverse in the space of real symmetric matrices. He obtained several properties but a “good” differential system was lacking. This was t...

Abstract Discrete analogues of the index transforms, involving Bessel and modified functions, are introduced investigated. The corresponding inversion theorems for suitable classes functions sequences established.