The Szegӧ kernel plays an important role in conformal mapping and satisfies a boundary Kerzman-Stein integral equation. The series representation for the Szegӧ kernel for an annulus region is well known. In this paper, the Adomian decomposition method is applied to solve the boundary Kerzman-Stein integral equation. The method provides another series form for the Szegӧ kernel for the annulus region. The two series are shown to be equivalent. Some numerical examples are also presented to compare the speed of convergence of the two series.
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