  The elastic $I=1/2$, $s$- and $p$-wave kaon-pion scattering amplitudes are
calculated using a single ensemble of anisotropic lattice QCD gauge field
configurations with $N_{\mathrm{f}} = 2+1$ flavors of dynamical Wilson-clover
fermions at $m_{\pi} = 230\mathrm{MeV}$. A large spatial extent of $L =
3.7\mathrm{fm}$ enables a good energy resolution while partial wave mixing due
to the reduced symmetries of the finite volume is treated explicitly.The
$p$-wave amplitude is well described by a Breit-Wigner shape with parameters
$m_{K^{*}}/m_{\pi} = 3.808(18)$ and $g^{\mathrm{BW}}_{K^{*}K\pi} = 5.33(20)$
which are insensitive to the inclusion of $d$-wave mixing and variation of the
$s$-wave parametrization. An effective range description of the near-threshold
$s$-wave amplitude yields $m_{\pi}a_0 = -0.353(25)$.
