  In this article, we obtain the explicit expression of the Casimir energy for
2-dimensional Clifford-Klein space forms in terms of the geometrical data of
the underlying spacetime with the help of zeta-regularization techniques. The
spacetime is geometrically expressed as a compact hyperbolic orbifold surface
that may have finitely many conical singularities. In computing the
contribution to the energy from a conical singularity, we derive an expression
of an elliptic orbital integral as an infinite sum of special functions. We
prove that this sum converges exponentially fast. Additionally, we show that
under a natural assumption (known to hold asymptotically) on the growth of the
lengths of primitive closed geodesics of the $(2, 3, 7)$-triangle group
orbifold its Casimir energy is positive (repulsive).
