Related papers: Differential Subordinations Involving Generalized …
We introduce and study the following special type of differential subordination implication: \begin{equation}\label{abs} p(z)Q(z)+\frac{zp'(z)}{\beta p(z)+\alpha}\prec h(z)\quad\Rightarrow p(z)\prec h(z), \end{equation} which generalizes…
In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New…
The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel…
We derive a normal ordering formula for the operator \((xI)^n\), where \(I\) denotes the Volterra operator. The resulting coefficients are shown to coincide with the Bessel numbers. We also present two applications, along with a…
In this article we introduce a new category of special functions called fundamental Bessel functions arising from the Voronoi summation formula for $\mathrm{GL}_n (\mathbb{R})$. The fundamental Bessel functions of rank one and two are the…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
In this article, we shall study fundamental Bessel functions for $\mathrm{GL}_n(\mathbb{F})$ arising from the Vorono\"i summation formula for any rank $n$ and field $\mathbb{F} = \mathbb{R}$ or $\mathbb{C}$, with focus on developing their…
In this paper our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kinds. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact…
We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced…
Partial Fourier transforms are used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the operator. In order to prove these…
The derivatives with respect to order {\nu} for the Bessel functions of argument x (real or complex) are studied. Representations are derived in terms of integrals that involve the products pairs of Bessel functions, and in turn series…
We consider the class $\mathcal{S}^*(q_c)$ of normalized starlike functions $f$ analytic in the open unit disk $|z|<1$ that satisfying the inequality \begin{equation*} \left|\left(\frac{zf'(z)}{f(z)}\right)^2-1\right|<c \quad (0<c\leq1).…
The article investigate the necessary and sufficient conditions for the normalized Bessel-struve kernel functions belonging to the classes $\mathcal{T}_\lambda(\alpha)$ , $\mathcal{L}_\lambda(\alpha)$. Some linear operators involving the…
We investigate the internal space of Bessel functions which is associated to the group Z of positive and negative integers defining their orders. As a result we propose and prove a new unifying formula (to be added to the huge literature on…
A finite transformation method is introduced. This method is equivalent to the $Z$ transform method to a certain extent but generalizes it. By applying the presented method to the Bessel functions, it is possible to solve related ordinary…
Using Jacobi's identity we derive a simple expression for the Bessel functions of integer order in terms of combinations of powers and hyperbolic functions of the same argument.
In a recent paper we unified Bessel functions of different orders .Here we extend the unification to other linairely independant solutions to Bessel equation, Neumann's and Hankel's functions
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the…