A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and a family of associated auxiliary polynomials, as transition elements between these families of functions. The consequences of this point of view a...

Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

In this study, our main objective is to determine some monotonic and log-concavity properties of generalized $k$-Bessel function by using its Hadamard product representation earlier results on power series. addition, the relationships between Bessel-type special functions basic functions, we present specific examples related trigonometric hyperbolic functions.

In this paper, we show that the matrix elements of some Lorentz group representation operators and bases transform acting in space may be expressed terms modified Bessel–Clifford functions their multi-index analogs introduced by authors via Delerue hyper Bessel functions.