Geodesic
Power Series Nonextendable Across the Boundary of their Convergence Domain
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 3, pp. 329-335

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In the article we construct a new power series in a single variable nonextendable through the boundary circle of the convergence disk. This series refines the known Fredholm`s example. Using this series we construct a double power series that does not admit an analytic continuation across the boundary of its convergence domain.
Keywords: power series, analitic continuation, infinitely differentiate, Dirichlet series. 
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     author = {Aleksandr D. Mkrtchyan},
     title = {Power {Series} {Nonextendable} {Across} the {Boundary} of their {Convergence} {Domain}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Aleksandr D. Mkrtchyan. Power Series Nonextendable Across the Boundary of their Convergence Domain. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 3, pp. 329-335. http://geodesic.mathdoc.fr/item/JSFU_2013_6_3_a5/