Suppose that d ∈ N and p > 0. In this paper, we study the generalized Bessel functions for the surface {v ∈ Rd : |v|p = 1}, introduced by D.St.P. Richards. We derive a recurrence relation for these functions and utilize a series representation to relate them to the classical symmetric functions. These generalized Bessel functions are symmetric with respect to the action of the hyperoctahedral g...

In this paper we complete and improve the study of the simulation of the hitting times of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous work [9], the authors introduced a new method for the simulation of hitting times for Bessel processes with integer dimension. The method, called walk on m...

The oblique incidence of a Bessel beam on a dielectric slab with refractive index n1 surrounded by a medium of a refractive index n > n1 may be studied simply by expanding the Bessel beam into a set of plane waves forming the same angle θ0 with the axis of the beam. In the present paper we examine a Bessel beam that impinges at oblique incidence onto a layer in such a way that each plane-wave c...

Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bes...

The standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument |z|, and to use an asymptotic series for large |z|. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [1] derived a series for an exp-arc integral which gave rise to an absolutely convergent series for the J and I Bessel functions with integral order. Such ser...

An identity in distribution due to F. Knight for Brownian motion is extended in two di erent ways: rstly by replacing the supremum of a re ecting Brownian motion by the range of an unre ected Brownian motion, and secondly by replacing the re ecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excurs...

An identity in distribution due to F. Knight for Brownian motion is extended in two diierent ways: rstly by replacing the supremum of a reeecting Brownian motion by the range of an unreeected Brownian motion, and secondly by replacing the reeecting Brownian motion by a recurrent Bessel process. Both extensions are explained in terms of random Brownian scaling transformations and Brownian excurs...

A compact representation of speech is possible using Bessel functions because of the similarity between voiced speech and the Bessel functions. Both voiced speech and the Bessel functions exhibit quasiperiodicity and decaying amplitude with time. In this paper, we have developed various feature extraction techniques using zero-order Bessel functions as basis functions for the task of closed-set...

Taking Bessel beams ~J0 beam! as a representation of a conical beam, and a slowly varying envelope approximation ~SVEA! we obtain the results for the theory of third-harmonic generation from an atomic medium. We demonstrate how the phenomenon of self-phase-matching is contained in the transverse-phasematching integral of the theory. A method to calculate the transverse-phase-matching integral c...

The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions ...