Knopp function is continuous
From specialfunctionswiki
Theorem
The Knopp function $K_{a,b}$ is continuous on $\mathbb{R}$ for $a \in (0,1)$ and $ab>1$.
The Knopp function $K_{a,b}$ is continuous on $\mathbb{R}$ for $a \in (0,1)$ and $ab>1$.