Dragana Jankov Maširević

On an identity for zeros of Bessel functions

In this paper our aim is to present an elementary proof of an identity of Calogero concerning the zeros of Bessel functions of the first kind. Moreover, by using our elementary approach we present a new identity for the zeros of Bessel functions of the first kind, which in particular reduces to some other new identities. We also show that our method can be applied for the zeros of other special functions, like Struve functions of the first kind, and modified Bessel functions of the second kind.

On New Formulas for the Cumulative Distribution Function of the Noncentral Chi-Square Distribution

The main aim of this article is to derive three new formulas for the cumulative distribution function of the noncentral chi-square distribution. The main advantage of such formulas is that they are given in terms of modified Bessel functions, leaky aquifer function and generalized incomplete gamma function which have a wide range of applications. In addition, the computational efficiency of the newly derived formulas versus already known formulas is established.

Bounds for the product of modified Bessel functions

In this note our aim is to present some monotonicity properties of the product of modified Bessel functions of the first and second kind. Certain bounds for the product of modified Bessel functions of the first and second kind are also obtained. These bounds improve and extend known bounds for the product of modified Bessel functions of the first and second kind of order zero. A new Turán type inequality is also given for the product of modified Bessel functions, and some open problems are stated, which may be of interest for further research.

Summations of Schlömilch series containing modified Bessel function of the second kind terms

The main aim of this article is to establish certain closed expressions for the Schlömilch series which members contain modified Bessel functions of the second kind and to obtain connection between special case of such series and a generalized Mathieu series. Closed expressions for the Schlömilch series with members containing products of and modified Bessel function of the first kind are derived as a by-product of these results.

Sampling bessel functions and bessel sampling

The main aim of this article is to establish summation formulae in form of sampling expansion series for Bessel functions Yv, Iv; and Kv, and obtain sharp truncation error upper bounds occurring in the Y-Bessel sampling series approximation. The principal derivation tools are the famous sampling theorem by Kramer and various properties of Bessel and modified Bessel functions which lead to the so-called Bessel sampling when the sampling nodes of the initial signal function coincide with a set of zeros of different cylinder functions.

p-Extended Mathieu Series from the Schlömilch Series Point of View

Motivated by certain current results by Pogány and Parmar [10] in which the authors introduced the so-called p-extended Mathieu series, the main aim of this paper is to present a connection between such series and various types of Schlömilch series.

Introduction and Preliminaries

We begin with a brief outline of special functions and methods, which will be needed in the next chapters. We recall here briefly the Gamma, Beta, Digamma functions, Pochhammer symbol, Bernoulli polynomials and numbers, Bessel, modified Bessel, generalized hypergeometric, Fox–Wright generalized hypergeometric, Hurwitz–Lerch Zeta functions, the Euler–Maclaurin summation formula together with Dirichlet series and Cahen’s formula, Mathieu series, Bessel and Struve differential equations, Fourier-Bessel and Dini series of Bessel functions and fractional differintegral.

Series of Bessel and Kummer-Type Functions

This book is devoted to the study of certain integral representations for Neumann, Kapteyn, Schlomilch, Dini and Fourier series of Bessel and other special functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques from the theory of differential equations. The text is aimed at a mathematical audience, including graduate students and those in the scientific community who are interested in a new perspective on Fourier–Bessel series, and their manifold and polivalent applications, mainly in general classical analysis, applied mathematics and mathematical physics.

Summations of Schlömilch series containing some Lommel functions of the first kind terms

ABSTRACTThe main aim of this article is to establish certain closed expressions for the Schlomilch series which members contain some Lommel functions of the first kind.ABSTRACT The main aim of this article is to establish certain closed expressions for the Schlömilch series which members contain some Lommel functions of the first kind.