It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess ‘universal’ Taylor series expansions about ζ; that is, partial sums ...
A power series that converges on the unit disc D is called universal if its partial sums approx-
imate arbitrary polynomials on arbitrary compacta in CnD that have connected complement.
This paper shows that such series ...
A holomorphic function on a planar domain Ω is said to possess a universal Taylor series about a point ζ of Ω if subsequences of the partial sums of the Taylor series approximate arbitrary polynomials on arbitrary compact ...
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 ...
It is known that, for any simply connected proper subdomain Ω of the complex plane and any point ζ in Ω, there are holomorphic functions on Ω that possess “universal” Taylor series expansions about ζ; that is, partial sums ...
It is known that, for any simply connected proper subdomain Omega of the complex plane and any point zeta in Omega, there are holomorphic functions on Omega that have "universal" Taylor series expansions about zeta; that ...