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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 allfunctions $f\in \mathcal{H}(\Omega)$ with the property that the set$\left\{T_N(f)(z)\coloneqq\sum_{n=0}^N\dfrac{f^{(n)}(z)}{n!} (-z)^n : N =0,1,2,\dots \right\}$ is dense in $\mathcal{H}(\Omega)$, then $S(\Omega)$ is adense $G_\delta$ set in $\mathcal{H}(\Omega)$. We answer the conjecture in theaffirmative in the special case where $\Omega$ is an open disc $D(z_0,r)$ thatdoes not contain $0$.

Universal partial sums of Taylor series as functions of the centre of expansion