Geodesic
Analytic continuation of power series by means of interpolating the coefficients by meromorphic functions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 173-183

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We study the problem of analytic continuation of a power series across an open arc on the boundary of the circle of convergence. The answer is given in terms of a meromorphic function of a special form that interpolates the coefficients of the series. We find the conditions for the sum of the series to extend analytically to a neigbourhood of the arc, to a sector defined by the arc, or to the whole complex plane except some arc on the convergence disk.
Keywords: Power series, analytic continuation, interpolating meromorphic function, indicator function. 
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     title = {Analytic continuation of power series by means of interpolating the coefficients by meromorphic functions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2015},
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Aleksandr J. Mkrtchyan. Analytic continuation of power series by means of interpolating the coefficients by meromorphic functions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 173-183. http://geodesic.mathdoc.fr/item/JSFU_2015_8_2_a6/