Geodesic
On continuation of~functions with polar singularities
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 377-384

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The main result is Theorem 1 . {\it If $f$ is a holomorphic function on the polydisk $'U\times U_n$ in $\mathbf C^n,$ and for each fixed $'a$ in some nonpluripolar set $E\subset{}'U$ the function $f('a,z_n)$ can be continued holomorphically to the whole plane with the exception of some polar set of singularities, then $f$ can be continued holomorphically to $('U\times\mathbf C)\setminus S,$ where $S$ is a closed pluripolar subset of $'U\times\mathbf C$.} Some generalizations are also given, along with corollaries on extension of functions with analytic sets of singularities. Bibliography: 13 titles. 
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     author = {A. S. Sadullaev and E. M. Chirka},
     title = {On continuation of~functions with polar singularities},
     journal = {Sbornik. Mathematics},
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     volume = {60},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_2_a7/}
}
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A. S. Sadullaev; E. M. Chirka. On continuation of~functions with polar singularities. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 377-384. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a7/