相关论文: Fourth-order Bessel-type special functions: a surv…
In this paper, we investigate some properties related to a multi-index special function $\mathcal{W}^{\left(\bar{\alpha},\bar{\nu}\right)}$ that arose from an eigenvalue problem for a multi-order fractional hyper-Bessel operator, involving…
We have used recent integral representations of the derivatives of the Bessel functions with respect to the order to obtain closed-form expressions in terms of generalized hypergeometric functions and Meijer-$G$ functions. Also, we have…
We investigate some fundamental properties of a peculiar class of special functions strictly related to Bessel, Anger and Weber functions, whose introduction was originally motivated by linear susceptibility tensor calculations in a hot,…
Discrete analogs of the index transforms with squares of Bessel functions of the first and second kind $J_\nu(z),\ Y_\nu(z)$ are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and…
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…
New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue…
In this paper, we are interested in a Neumann-type series for modified Bessel functions of the first kind which arises in the study of Dunkl operators associated with dihedral groups and as an instance of the Laguerre semigroup constructed…
Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite integrals involving monomials in $x$…
We prove uniqueness and give precise criteria for existence of split and non-split Bessel models for a class of lowest and highest weight representations of the groups GSp(4,R) and Sp(4,R) including all holomorphic and anti-holomorphic…
We use a degeneration of the 1D double affine Hecke algebra and the Dunkl operator to study systematically nonsymmetric Bessel functions and their truncations.
We find that the solution of the polar angular differential equation can be written as the universal associated Legendre polynomials. Its generating function is applied to obtain an analytical result for a class of interesting integrals…
New index transforms of the Lebedev type are investigated. It involves the real part of the product of the modified Bessel functions as the kernel. The boundedness and invertibility are examined for these operators in the Lebesgue weighted…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
Sufficient conditions are determined on the parameters such that the generalized and normalized Bessel function of the first kind and other related functions belong to subclasses of starlike and convex functions defined in the unit disk…
This paper was published in the special issue of the Journal of Inequalities and Special Functions dedicated to Professor Ivan Dimovski's contributions to different fields of mathematics: transmutation theory, special functions, integral…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
In this work, we introduce bicomplex Bessel function and analyze its region of convergence. Important properties of the bicomplex Bessel function, such as recurrence relations, integral representations, differential relations are explored.…
In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or Hyper-Bessel-type operators. We discuss then the…
The Bessel-Neumann expansion (of integer order) of a function $g:\mathbb{C}\rightarrow\mathbb{C}$ corresponds to representing $g$ as a linear combination of basis functions $\phi_0,\phi_1,\ldots$, i.e., $g(z)=\sum_{\ell = 0}^\infty w_\ell…
We develop techniques at the interface between differential algebra and model theory to study the following problems of exponential algebraicity: Does a given algebraic differential equation admits an exponentially algebraic solution, that…