By applying Olver's uniform representation for Bessel
and Hankel functions of complex order , the sought poles [v.sub.k] for the two analyzed cases are found by plotting the denominators of (5) as functions of complex variable and searching for their zeros.
There are some special light beams, called nondiffraction beam, can keep its beam profile during propagation, like Bessel
beams , Airy beams , and so on.
When p = 1, 2, ..., N - 1, the summation subscript / must take both 1 and 3 to obtain the complete solution of the vector wave functions, since the first-kind spherical Bessel
function and the third-kind spherical Bessel
function (or sometimes referred to as the first-kind spherical Hankel function) are regular in these regions; however, when p = N, the summation subscript J only takes 1 due to the singularity of the second-kind spherical Bessel
function (and hence the third-kind spherical Bessel
function) at the origin.
where [w.sub.0] is the waist width of the Gaussian beam, [k.sub.r] is the radial wave vector, and [J.sub.m] (x) is an mth order Bessel
function of first kind.
In this paper we investigate the discrete version of Bessel
processes defined by an stochastic differential equation.
This week they beat Elton Rigger 10-0 with goals courtesy of James Harris (4), Lee Dermody (3), Tom Harris (2) and Robbie Bessel
This article studies the generalized Bessel
function [u.sub.p](z) = [u.sub.p,b,c](z) given by the power series
are extensively studied by Altinates and Owa and certain conditions for hypergeometric function and generalized Bessel
functionf for these classes were studied by Mostafa and Porwal and Dixit.
Dr Pance Naumov, associate professor of chemistry at New York University Abu Dhabi (NYUAD), has been awarded the Friedrich Wilhelm Bessel
Research Award in recognition of his research achievements.
Remark on Sturm bounds for Siegel modular forms of degree 2 Toshiyuki KIKUTA Generalized Bessel
transform of (beta],[gamma])-generalized Bessel
Lipschitz functions Radouan DAHER and Mohamed EL HAMMA Above two, communicated by Kenji FUKAYA, M.J.A.
Houston, TX, February 13, 2015 --(PR.com)-- University of Houston (UH) developmental psychology professor Arturo Hernandez is among this year's recipients of the Friedrich Wilhelm Bessel