On the construction of generalized monogenic Bessel polynomials

Abstract

MSC Classification: 30G35; 33C45In recent years, much attention has been paid to the role of classical special functions of a real or complex variable in mathematical physics, especially in boundary value problems (BVPs). In the present paper, we propose a higher-dimensional analogue of the generalized Bessel polynomials within Clifford analysis via a special set of monogenic polynomials. We give the definition and derive a number of important properties of the generalized monogenic Bessel polynomials (GMBPs), which are defined by a generating exponential function and are shown to satisfy an analogue of Rodrigues' formula. As a consequence, we establish an expansion of particular monogenic functions in terms of GMBPs and show that the underlying basic series is everywhere effective.We further prove a second-order homogeneous differential equation for these polynomials.

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

“…Remark 2.2. If the matrix F, L ∈ C 1×1 = C, then the generalized Bessel matrix polynomial in (2.15) reduces to generalized Bessel polynomial in [10][11][12].…”

“…In [4], extension to the matrix framework of the classical families of Legendre, Laguerre, Jacobi, Chebyshev, Gegenbaner and Hermite polynomials have been introduced. Meanwhile, one particular orthogonal polynomials which frequently appears in the recent studies and applications [10][11][12], is the generalized Bessel polynomials, which in its matrix form is also defined in [4,13]. Later on, distinct works of the generalized Bessel matrix polynomials have been discussed (see [14][15][16][17]).…”

On Behavior Laplace Integral Operators with Generalized Bessel Matrix Polynomials and Related Functions

“…Recently, these polynomials have been investigated in diverse ways and turned out to be applicable in a number of research fields (see, to exemplify, [22][23][24][25]).…”

On the representation of monogenic functions by the product bases of polynomials

“…From this starting point, many results on the polynomial bases in the complex case of one complex variable were refined and generalized to the Clifford setting (see [1][2][3][4][5][6][7][8][9]27]). In this line of research in Clifford setting, one of the interesting problem has been investigated by Zayed et al [32] where the authors explored the effectiveness of the hypercomplex derivative and primitive basic sets associated with the previously mentioned polynomials.…”

“…Recently, these polynomials were used to prove a counterpart of Hadamard's three-hyperballs theorem within Clifford analysis and to establish an overconvergence property of a special monogenic simple series (see [9]). As an application of this overconvergence property on generalized monogenic Bessel polynomials, we refer to [1] .…”