We demonstrate the generation of Bessel beams using an acousto-optic array based on a liquid filled cavity surrounded by a cylindrical multi-element ultrasound transducer array. Conversion of a Gaussian laser mode into a Bessel beam with tunable order and position is shown. Also higher-order Bessel beams up to the fourth order are successfully generated with experimental results very closely ma...

Two representations of the extended gamma functions Γ 2,0 0,2 [(b, x)] are proved. These representations are exploited to find a transformation relation between two Fox's H-functions. These results are used to solve Fox's H-function in terms of Meijer's G-function for certain values of the parameters. A closed form representation of the kernel of the Bessel type integral transform is also proved.

This paper is part of the collection initiated in [12], aiming to evaluate the entries in [8] and to provide some context. This table contains a large variety of entries involving the Bessel functions. The goal of the current work is to evaluate some entries in [8] where the integrand is an elementary function and the result involves the so-called modified Bessel function of the second kind, de...

Given an orthogonal polynomial sequence on the real line, another of polynomials can be found by composing them with a Möbius transformation. In this work, we study properties such Möbius-transformed in systematically way. We show that these are given curve complex plane respect to particular kind varying measure, and they enjoy several common line. Moreover, many easier derived from approach, ...

A closed integral expression is derived for Neumann series of Bessel functions — a series of Bessel functions of increasing order — over the set of real numbers.

In the framework of Sobolev (Bessel potential) spaces Hn(R,R or C), we consider the nonlinear Nemytskij operator sending a function x ∈ R 7→ f(x) into a composite function x ∈ R 7→ G(f(x), x). Assuming sufficient smoothness for G, we give a ”tame” bound on the Hn norm of this composite function in terms of a linear function of the Hn norm of f , with a coefficient depending on G and on the Ha n...

In the framework of Sobolev (Bessel potential) spaces Hn(R,R or C), we consider the nonlinear Nemytskij operator sending a function x ∈ R 7→ f(x) into a composite function x ∈ R 7→ G(f(x), x). Assuming sufficient smoothness for G, we give a ”tame” bound on the Hn norm of this composite function in terms of a linear function of the Hn norm of f , with a coefficient depending on G and on the Ha n...

In this paper, we give some conditions under which the finite sum of continuous $g$-frames is again a continuous $g$-frame. We give necessary and sufficient conditions for the continuous $g$-frames $Lambda=left{Lambda_w in Bleft(H,K_wright): win Omegaright}$ and $Gamma=left{Gamma_w in Bleft(H,K_wright): win Omegaright}$ and operators $U$ and $V$ on $H$ such that $Lambda U+Gamma V={Lambda_w U+Ga...