  In this paper, we establish Basmajian's identity for $(1,1,2)$-hyperconvex
Anosov representations from a free group into $PGL(n, R)$. We then study our
series identities on holomorphic families of Cantor non-conformal repellers
associated to complex $(1,1,2)$-hyperconvex Anosov representations. We show
that the series is absolutely summable if and only if the Hausdorff dimension
of the Cantor set is strictly less than one. Throughout the domain of
convergence, these identities can be analytically continued and they exhibit
nontrivial monodromy.
