Abstract
By reflections, we obtain the Schwarz–Poisson formula in a sector with angle \({\vartheta=\frac{\pi}{n},\,n\in \mathbb{N}}\) , which is a generalization of the corresponding result obtained by Begehr and Vaitekhovich (Funct Approx 40(2):251–282, 2009). Especially, boundary behaviors at corner points are discussed in detail. Then we consider the Schwarz and Dirichlet boundary-value problems (BVPs) for the Cauchy–Riemann equation, and expressions of solution and the condition of solvability are explicitly obtained.
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