$r \mapsto \arctan r$ on $[0, \infty)$
Terms
| Term | This example | Why |
|---|---|---|
| class-$\mathcal{K}$ | ✓ | |
| positive definite function | ✓ | $r \mapsto \arctan r$ is of class $\mathcal{K}$ because it is continuous, increasing, and zero at $0$, and it is positive definite. It is not of class $\mathcal{K}_{\infty}$, because it is bounded by $\pi / 2$. |
| class-$\mathcal{K}_\infty$ | ✗ |