We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute the nth Laguerre-type derivatives of a composite function. Incidentally, we generalize a result considered by L. Carlitz in order to obtain explicit relationships between Bessel functions and gener...

We give some interest in radial Dunkl processes associated with dihedral systems. We write down the semi group density and as a by-product the generalized Bessel function and the W -invariant generalized Hermite polynomials. Then, a skew product decomposition, involving only independent Bessel processes, is given and the tail distribution of the first hitting time of boundary of the Weyl chambe...

In the present article, using generalized Bessel-Maitland transform, Laplace transform and other known transforms, authors obtain new Parseval-Goldstein type relations. Using these relations, some integrals involving Fox-Wright functions are evaluated. Illustrative examples also given.

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.

We introduce a family of number triangles defined by exponential Riordan arrays, which generalize Pascal’s triangle. We characterize the row sums and central coefficients of these triangles, and define and study a set of generalized Catalan numbers. We establish links to the Hermite, Laguerre and Bessel polynomials, as well as links to the Narayana and Lah numbers.

The Bessel–Struve kernel function defined in the unit disc is used this study. functions are generalized article, and differential equations derived. We found conditions under which Lemniscate convex by using a subordination technique. relation between Janowski class exponential also

In this paper, we prove two estimates useful in applications for the Fourier-Bessel transform space Lp(R2+,x2?1+1y2?2+1dxdy), (1 < p ? 2), as applied to some classes of functions characterized by a generalized modulus continuity.

Introduction/purpose: The aim of this article is to establish integral transforms the generalized Lommel-Wright function. Methods: These are expressed in terms Wright Hypergeometric Results: Integrals involving trigonometric, Bessel function and Struve functions obtained. Conclusions: Various interesting as consequence method

In this paper, circular Lorentz–Bessel–Gaussian beams (CLBGBs) are introduced as a novel member of the Lorentz-Gaussian family. The analytical expression propagation these passing through paraxial optical ABCD system is derived. generalized Huygens-Fresnel diffraction integral form Collins’s formula and expansion Lorentz distribution in terms complete orthonormal basis set Hermite-Gauss modes u...