Related papers: Differential subordinations and superordinations f…
This survey paper reports on the properties of the fourth-order Bessel-type linear ordinary differential equation, on the generated self-adjoint differential operators in two associated Hilbert function spaces, and on the generalisation of…
A bi-univalent function is a univalent function defined on the unit disk with its inverse also univalent on the unit disk. Estimates for the initial coefficients are obtained for bi-univalent functions belonging to certain classes defined…
Let $q_1$ and $q_2$ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions $p$ to satisfy the double…
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).…
Reformulated uniform asymptotic expansions are derived for ordinary differential equations having a large parameter and a simple turning point. These involve Airy functions, but not their derivatives, unlike traditional asymptotic…
We prove explicit uniform two-sided bounds for the phase functions of Bessel functions and of their derivatives. As a consequence, we obtain new enclosures for the zeros of Bessel functions and their derivatives in terms of inverse values…
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
Based on operator algebras commonly used in quantum mechanics some properties of special functions such as Hermite and Laguerre polynomials and Bessel functions are derived.
The primary objective of this work is to obtain some sufficient conditions so that normalized Gauss hypergeometric function satisfies exponential starlikeness and convexity in the unit disk. Moreover, conditions on parameter of this…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…
In this paper, we introduce a subclass of p-valent non-bazilavec functions of order. Some subordination relations and the inequality properties of p-valent functions are discussed. The results presented here generalize and improve some…
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…
We write down the generalized Bessel function associated with the root system of type $D$ by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type $D$.
A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized…
Our objective in this paper is to introduce and investigate comprehensive-constructed subclasses of normalized analytic and bi-univalent functions on the unit open disc. Bounds for the second and third Tayler-Maclaurin coefficients of…
Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.
The object of this paper is to study relationship between successive coefficients of some subclasses of the class of univalent functions in the unit disk. the result obtained is sharp, and is used to provide a new, short proof of the…
In this paper necessary and sufficient conditions are deduced for the starlikeness of Bessel functions of the first kind and their derivatives of the second and third order by using a result of Shah and Trimble about transcendental entire…
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…