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It is known that, for any simply connected proper subdomain of the complex plane and any point in , there are holomorphic functions on that have universalTaylor series expansions about ; that is, partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compacta in Cn that have connected complement. This note shows that this… (More)

- N. Tsirivas
- 2017

The known proofs for universal Taylor series do not determine a specific universal Taylor series. In the present paper, we isolate a specific universal Taylor series by modifying the proof in [30]. Thus we determine all Taylor coefficients of a specific universal Taylor series on the disc or on a polygonal domain. Furthermore in non simply connected… (More)

- G. Costakis, N. Tsirivas
- Journal of Approximation Theory
- 2014

For a holomorphic function f in the unit disk, Sn(f) denotes the n-th partial sum of the Taylor development of f with center at 0. We show that given a strictly increasing sequence of positive integers (λn), there exists a holomorphic function f on the unit disk such that the pairs of partial sums {(Sn(f), Sλn(f)) : n = 1, 2, . . .} approximate all… (More)

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