  Measurements of the differential branching fraction and angular moments of
the decay $B^0 \to K^+ \pi^- \mu^+ \mu^-$ in the $K^+\pi^-$ invariant mass
range $1330<m(K^+ \pi^-)<1530~MeV/c^2$ are presented. Proton-proton collision
data are used, corresponding to an integrated luminosity of 3 $fb^{-1}$
collected by the LHCb experiment. Differential branching fraction measurements
are reported in five bins of the invariant mass squared of the dimuon system,
$q^2$, between 0.1 and 8.0 $GeV^2/c^4$. For the first time, an angular analysis
sensitive to the S-, P- and D-wave contributions of this rare decay is
performed. The set of 40 normalised angular moments describing the decay is
presented for the $q^2$ range 1.1--6.0 $GeV^2/c^4$.
