Two-dimensional generalization of the N\"{o}rlund theorem for branched continued fractions
speaker: Nataliya Hoyenko (Pidstryhach Institute for Applied Problems in Mechanics and Mathematics of NASU Lviv, Naukova Str., 3-b, Ukraine 79060)abstract: The two-dimensional generalization of the one-dimensional N\"{o}rlund theorem on the convergence and the correspondence of the continued fraction, which is the expansion for the ratios of the hypergeometric functions, is obtained. New recurrence relations for the two-variable Appell hypergeometric function $F1$ are constructed. The expansions of ratios of these functions into the branched continued fractions (BCF) of the N\"{o}rlund type are built using these relations. The correspondence of BCF to a formal double power series, which represents a function of interest, is studied. The correspondence principle of sequence of rational functions of two variables to formal double power series is proved. This principle is a new powerful tool to prove convergence of BCF to a given function. The convergence domains of BCF are investigated.
timetable:
Thu 13 Jun, 15:00 - 15:25, Aula Dini
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