\(H\)-regularity of functions with values in Cayley algebra based on a generalized axially symmetric potential theory operator (Q2891115)

The authors discuss notions of regularity for octonionion-valued functions. Notions based on generalizations of the standard Cauchy-Riemann operator/octonionic Cauchy-Riemann operator and the \(H\)-regularity of Leutwiler are considered with their respective properties in terms of characterizations in terms of coordinate functions, composition, and quasi-conformality. In the end power series expansions in terms of an octonionic variable are considered for \(H\)-regular functions.