In this paper we consider the question of continuation of the sums of the Hartogs series that admit holomorphic continuation along a fixed direction with “thin” singularities, assuming only the holomorphic of the coefficients of the series and investigate the convergence region of such series. The results of the work develop a well-known result of A.Sadullaev and E.M.Chirka on the continuation of functions with polar singularities.
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Tuychiev, Takhir and Tishabaev, Jurabay
"On the continuation of the Hartogs series with holomorphic coefficients,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 2:
1, Article 5.