  We discuss finite-size corrections to the spiky strings in $AdS$ space which
is dual to the long $\mathcal{N}=4$ SYM operators of the form Tr($\Delta_+
^{J_1}\phi_1\Delta_+ ^{J_2}\phi_2...\Delta_+ ^{J_n}\phi_n$). We express the
finite-size dispersion relation in terms of Lambert $\mathbf{W}$-function. We
further establish the finite-size scaling relation between energy and angular
momentum of the spiky string in presence of mixed fluxes in terms of
$\mathbf{W}$-function. We comment on the solution in pure NS-NS background as
well.
