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Register a new userUniversal partial sums of Taylor series as functions of the centre of expansion
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Authors
Christoforos Panagiotis
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V. Nestoridis conjectured that if $Omega$ is a simply connected subset of $mathbb{C}$ that does not contain $0$ and $S(Omega)$ is the set of all functions $fin mathcal{H}(Omega)$ with the property that the set $left{T_N(f)(z)coloneqqsum_{n=0}^Ndfrac{f^{(n)}(z)}{n!} (-z)^n : N = 0,1,2,dots right}$ is dense in $mathcal{H}(Omega)$, then $S(Omega)$ is a dense $G_delta$ set in $mathcal{H}(Omega)$. We answer the conjecture in the affirmative in the special case where $Omega$ is an open disc $D(z_0,r)$ that does not contain $0$.
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