In the present paper we consider the heat equation ut = Lu where L is a second-order difference operator in a discrete variable n. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients αk(n,m) in this expansion are analogs of Hadamard’s coefficients for the (continuous) Schrödinger operator. We derive an explicit formula for αk in ter...

In this paper, we first discuss about canonical dual of g<span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...

We examine the three-dimensional intensity distribution of vector Bessel-Gauss beams with general polarization near the focus of a nonaperturing thin lens. Recently reported linearly and azimuthally polarized Bessel-Gauss beams are members of this family. We define the width and focal plane of such a vector beam using an encircled-energy criterion and calculate numerically that, as for scalar b...

A few transformations are presented for reducing certain cases of Meijer’s Gfunction to a G-function of lower order. Their applications to the integration of a product of Bessel functions are given. The algorithm has been implemented within Mathematica 3.0.

Abstract We introduce two extensions of the canonical Feller–Spitzer distribution from class Bessel densities, which comprise distinct stochastically decreasing one-parameter families positive absolutely continuous infinitely divisible distributions with monotone whose upper tails exhibit a power decay. The densities members first are expressed in terms modified function kind, whereas second ha...

The generalized Stirling numbers Ss;h(n, k) introduced recently by the authors are shown to be a special case of the three parameter family of generalized Stirling numbers S(n, k;α, β, r) considered by Hsu and Shiue. From this relation, several properties of Ss;h(n, k) and the associated Bell numbers Bs;h(n) and Bell polynomials Bs;h|n(x) are derived. The particular case s = 2 and h = −1 corres...