  We study conformal partial waves (CPWs) in Mellin space with totally
symmetric external operators of arbitrary integer spin. The exchanged spin is
arbitrary, and includes mixed symmetry and (partially)-conserved
representations. In a basis of CPWs recently introduced in arXiv:1702.08619, we
find a remarkable factorisation of the external spin dependence in their Mellin
representation. This property allows a relatively straightforward study of
inversion formulae to extract OPE data from the Mellin representation of
spinning 4pt correlators and in particular, to extract closed-form expressions
for crossing kernels of spinning CPWs in terms of the hypergeometric function
${}_4F_3$. We consider numerous examples involving both arbitrary internal and
external spins, and for both leading and sub-leading twist operators. As an
application, working in general $d$ we extract new results for ${\cal
O}\left(1/N\right)$ anomalous dimensions of double-trace operators induced by
double-trace deformations constructed from single-trace operators of generic
twist and integer spin. In particular, we extract the anomalous dimensions of
double-trace operators $[\mathcal{O}_J\Phi]_{n,l}$ with ${\cal O}_J$ a
single-trace operator of integer spin $J$.
