  We compute anomalous dimensions of higher spin operators in Conformal Field
Theory at arbitrary space-time dimension by using the OPE inversion formula of
\cite{Caron-Huot:2017vep}, both from the position space representation as well
as from the integral (viz. Mellin) representation of the conformal blocks. The
Mellin space is advantageous over the position space not only in allowing to
write expressions agnostic to the space-time dimension, but also in that it
replaces tedious recursion relations in terms of simple sums which are easy to
perform. We evaluate the contributions of scalar and spin exchanges in the
$t-$channel exactly, in terms of higher order Hypergeometric functions. These
relate to a particular exchange of conformal spin $\beta=\Delta+J$ in the
$s-$channel through the inversion formula. Our exact results reproduce the
special cases for large spin anomalous dimension and OPE coefficients obtained
previously in the literature.
