Solution
= Solution
\b[Yes:] take the <unnormalized sinc function> with its removable value at zero,
$$
\boxed{g(z)=\begin{cases}\sin z/z,&z\ne0,\\1,&z=0.\end{cases}}
$$
Its <power series> is $\sum_{m=0}^\infty(-1)^mz^{2m}/(2m+1)!$, with infinite <radius of convergence>, so it is an <entire function>. At $z=1/n$ it gives $n\sin(1/n)$ as required. The <identity theorem> also proves this entire solution is unique.