  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 $f\in \mathcal{H}(\Omega)$ 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 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 $0$.
