We introduce an exact analytical solution of the homogeneous space-fractional Helmholtz equation in cylindrical coordinates. This solution, called vector Space-Fractional Bessel Beam (SFBB), has been established from Lorenz' gauge condition and Hertz transformations. perform scalar wave analysis focusing on electromagnetics applications, especially cases where dimensions beam are comparable to ...

Keywords: Generalized Marcum Q-function Non-central chi and chi-squared distribution Modified Bessel functions Log-concavity NBU property a b s t r a c t In this paper, we consider the generalized Marcum Q-function of order m > 0 real, defined by Q m ða; bÞ ¼ 1 a mÀ1 Z 1 b t m e À t 2 þa 2 2 I mÀ1 ðatÞdt; where a; b P 0, I m stands for the modified Bessel function of the first kind and the righ...

In this paper, we first show that the tensor product of a finite number of standard g-frames (resp. fusion frames, frames) is a standard g-frame (resp. fusion frame, frame) for the tensor product of Hilbert $C^ast-$ modules and vice versa, then we consider tensor products of g-Bessel multipliers, Bessel multipliers and Bessel fusion multipliers in Hilbert $C^ast-$modules. Moreover, we obtain so...

In the present paper, we define a new representation for Voigt function involving the product of generalized Bessel function and Whittaker function. We first obtain its explicit representation and then we derive partly bilateral and partly unilateral representations for this function. Further, we establish some new and interesting generating functions involving various hypergeometric functions ...

In this note we consider the D optimal design problem for the heteroscedastic polynomial regression model Karlin and Studden a found explicit solutions for three types of e ciency functions We introduce two new functions to model the heteroscedastic structure for which the D optimal designs can also be found explicitly The optimal designs have equal masses at the roots of generalized Bessel pol...

Abstract. We work out the expression of the generalized Bessel function of B2-type derived in [4]. This is done using Dijskma and Koornwinder’s product formula for Jacobi polynomials and the obtained expression is given by multiple integrals involving only a normalized modified Bessel function and two symmetric Beta distributions. We think of that expression as the major step toward the explici...

The transient analysis of a queuing system with fixed-size batch Poisson arrivals and a single server with exponential service times is presented. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. These functions are shown to be a generalization of the modified Bessel functions of the first kind, with the batch siz...

Motivated by G. H. Hardy's 1939 results [4] on functions orthogonal with respect to their real zeros λn, n = 1, 2,. .. , we will consider, within the same general conditions imposed by Hardy, functions satisfying an orthog-onality with respect to their zeros with Jacobi weights on the interval (0, 1), that is, the functions f (z) = z ν F (z), ν ∈ R, where F is entire and Z 1 0 f (λnt)f (λmt)t α...