Two methods are investigated for the time-domain simulation of functions and dynamical systems of Bessel type, involved in wave propagation (see e.g. [1], [8], [2]). Both are based on complex analysis and lead to finitedimensional approximations. The first method relies on optimized parametric contours and provides asymptotic convergence rates. The second is based on cuts and integral represent...

We find low order approximations to the spherical nonreflecting boundary kernel for the wave equation in three dimensions. First we express the Laplace transform of the kernel as a rational function by solving for the zeros of a modified Bessel function. Then we formulate a linear time-invariant dynamical system whose transfer function is this rational function. Finally we use the Balanced Trun...

We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly periodic Mathieu functions in azimuth, depend on a field strength parameter. When the parameter is zero, pendulum beams are Bessel beams, and as the parameter approaches infinity, they res...

Discrete analogs of the Lebedev–Skalskaya transforms are introduced and investigated. It involves series integrals with respect to kernels Re Kα+in(x),Im Kα+in(x),x>0,n∈N,|α|<1, i is imaginary unit Kν(z) modified Bessel function. The corresponding inversion formulas for suitable functions sequences in terms these established when α=±1/2. case α=0 reduces Kontorovich–Lebedev transform.

This paper provides tools for the study of the Dirichlet random walk in R . We compute explicitly, for a number of cases, the distribution of the random variableW using a form of Stieltjes transform ofW instead of the Laplace transform, replacing the Bessel functions with hypergeometric functions. This enables us to simplify some existing results, in particular, some of the proofs by Le Caër (2...

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

We examine some recent results of Bownik on density and connectivity of the wavelet frames. We use orthogonality (strong disjointness) properties of frame and Bessel sequences, and also properties of Bessel multipliers (operators that map wavelet Bessel functions to wavelet Bessel functions). In addition we obtain an asymptotically tight approximation result for wavelet frames.

We give an analytical expression for the joint Laplace transform of the L and L norms of a 3-dimensional Bessel bridge. We derive the results by using merely probabilistic arguments. More precisely we show that the law of this functional is closely connected with the one of the first passage time of an Ornstein Uhlenbeck process. The motivation for studying such problem are multiple. As an inst...

The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process PD(α, θ). Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy– Stieltjes transform are achieved. Moreover, several interesting integral identities are obtained by exploiting a correspondence betw...

Recently, the authors introduced least squares quantization table (LSQT) method to accelerate the direct Fourier transform to reconstruct magnetic resonance images acquired using a spiral trajectory. In this paper, we will discuss the LSQT further in its adaptability, reusability and choice of the number of groups. The experimental results show that the LSQT method has better adaptability for t...