Related papers: Tur\'an determinants of Bessel functions

A new counterpart of Bessel's inequality for orthornormal families in real or complex inner product spaces is obtained. Applications for some Gruss type results are also provided.

We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for…

We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and…

We study a number of possible extensions of the Ramanujan master theorem, which is formulated here by using methods of Umbral nature. We discuss the implications of the procedure for the theory of special functions, like the derivation of…

In this paper we consider a new nonlinear mathematical model for corneal topography formulated as two-point boudary value problem. We derive it from first physical principles and provide some mathematical analysis. The existence and…

We examine convergent representations for the sum of Bessel functions \[\sum_{n=1}^\infty \frac{J_\mu(na) J_\nu(nb)}{n^{\alpha}}\] for $\mu$, $\nu\geq0$ and positive values of $a$ and $b$. Such representations enable easy computation of the…

A decoupling type inequality for a sum of functions of Guassian vectors is established.

The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…

Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.

This paper deals with both the higher order Tur\'an inequalities and the Laguerre inequalities for quasi-polynomial-like functions -- that are expressions of the form $f(n)=c_l(n)n^l+\cdots+c_d(n)n^d+o(n^d)$, where $d,l\in\mathbb{N}$ and…

Differential subordination and superordination preserving properties for univalent functions in the open unit disk with an operator involving generalized Bessel functions are derived. Some particular cases involving trigonometric functions…

This paper introduces and studies a generalization of the $\mathtt{k}$-Bessel function of order $\nu$ given by \[\mathtt{W}^{\mathtt{k}}_{\nu, c}(x):= \sum_{r=0}^\infty \frac{(-c)^r}{\Gamma_{\mathtt{k}}\left( r \mathtt{k}…

Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

In this paper, we obtained some new Ostrowski-Gruss type inequalities contains twice differentiable functions.

In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $t_{\mu,\nu}(x)$. In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality,…

In this contribution we first summarize how contour integration methods can be used to derive closed formulae for functional determinants of ordinary differential operators. We then generalize our considerations to partial differential…

Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…

We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the…

We study the relation between the coefficients of Taylor series and Kapteyn series representing the same function. We compute explicit formulas for expressing one in terms of the other and give examples to illustrate our method.

The paper aims to establish the Tur\'an inequalities, the Laguerre inequalities (order $2$), and the determinantal inequalities (order $3$) for $\Delta p(n)$ and $\Delta \bar{p}(n)$, where $\Delta f(n)$ is the first-order forward difference…