On Riemann problems for single‐periodic polyanalytic functions

In this article, Riemann‐type boundary‐value problem of single‐periodic polyanalytic functions has been investigated. By the decomposition of single‐periodic polyanalytic functions, the problem is transformed into n equivalent and independent Riemann boundary‐value problems of single‐periodic analytic functions, which has been discussed in details according to two growth orders of functions. Finally, we obtain the explicit expression of the solution and the conditions of solvability for Riemann problem of the single‐periodic polyanalytic functions.