  The quantum vacuum energy for a hybrid comb of Dirac $\delta$-$\delta'$
potentials is computed using the energy of the single $\delta$-$\delta'$
potential over the real line that makes up the comb. The zeta function of a
comb periodic potential is the continuous sum of zeta functions over the dual
primitive cell of Bloch quasi-momenta. The result obtained for the quantum
vacuum energy is non-perturbative in the sense that the energy function is not
analytical for small couplings
