A Cauchy Integral Formula for Infrapolymonogenic Functions in Clifford Analysis

In this paper we derive a Cauchy integral representation formula for the solutions of the iterated sandwich equation ∂x̲2k-1f∂x̲=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\partial _{{\underline{x}}}^{2k-1}f\partial _{{\underline{x}}}=0$$\end{document}, where k is a positive integer and ∂x̲\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\partial _{{\underline{x}}}$$\end{document} stands for the Dirac operator in the Euclidean space Rm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {R}}}^m$$\end{document}. We call these solutions (2k-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(2k-1)$$\end{document}-infrapolymonogenic functions (or simply infrapolymonogenic if no confusion can arise). For k=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k=1$$\end{document} the derived formula becomes the Cauchy integral representation formula recently obtained in Moreno-García et al. (Adv Appl Clifford Algebras 27(2):1147–1159, 2017) for inframonogenic functions.