  We identify the maximal real interval on which $\sin_{p,n}$ is real-analytic
for any real number $p>1$ and any integer $n>1$. We achieve this by first
proving that $\sin_{p,n}$ is analytic at $(1/2){\pi}_{p,n}$ iff $p=m/(m-1)$ for
some integer $m>1$, in which case we determine the radius of convergence of the
Taylor series at $(1/2){\pi}_{p,n}$.
