The Bessel-Clifford Function Associated to the Cayley-Laplace Operator

In this paper the Cayley-Laplace operator Delta xu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta _{xu}$$\end{document} is considered, a rotationally invariant differential operator which can be seen as a generalisation of the classical Laplace operator for functions depending on wedge variables Xab\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_{ab}$$\end{document} (the minors of a matrix variable). We will show that the Bessel-Clifford function appears naturally in the framework of two-wedge variables, and explain how this function somehow plays the role of the exponential function in the framework of Grassmannians. This will be used to obtain a generalisation of the series expansion for the Newtonian potential, and to investigate a new kind of binomial polynomials related to Nayarana numbers.