Abstract
In 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.