Geodesic
On functions of several complex variables that are separately meromorphic
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 481-489

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In this paper it is proved that a function of $n$ complex variables that is meromorphic in each variable separately on a special set $X$ is globally meromorphic in the neighborhood of $X$. This result is an analog of a theorem of J. Siciak on separate holomorphicity. Bibliography: 8 titles. 
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     author = {M. V. Kazaryan},
     title = {On functions of several complex variables that are separately meromorphic},
     journal = {Sbornik. Mathematics},
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     volume = {28},
     number = {4},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_4_a2/}
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M. V. Kazaryan. On functions of several complex variables that are separately meromorphic. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 481-489. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a2/