Slice Polyanalytic Functions
摘要
The theory of polyanalytic functions is an interesting topic in complex analysis studied since over a century. It extends the concept of holomorphic functions to nullsolutions of higher order powers of the Cauchy-Riemann operator. The definition can also be extended to the hypercomplex case, in particular to the quaternionic case, by using the idea of slice hyperholomorphicity or to the more classical theory of Cauchy-Fueter regularity.