Cauchy–Riemann operator in Cayley–Dickson–Clifford analysis

In this paper, we apply the Cayley–Dickson process on the real Clifford algebra \(\mathbb {R}_{0,n}\) ${\mathbb{R}}_{0,n}$ to obtain the so called Cayley–Dickson–Clifford algebra C–D- \(\mathbb {R}_{0,n}\) ${\mathbb{R}}_{0,n}$ . We introduce a Cauchy–Riemann operator for functions taking values in C–D- \(\mathbb {R}_{0,n}\) ${\mathbb{R}}_{0,n}$ . This direction connects to both octonion analysis and Clifford analysis. It covers octonion analysis, quaternion analysis and the theory of biregular functions in Clifford analysis.