  In the presence of both direct and indirect unitarity violation in the lepton
mixing matrix, we derive a complete set of series expansion formulas for
neutrino oscillation probabilities in matter of constant density. Expansions in
the mass hierarchy parameter $\alpha \equiv \Delta m_{21}^{2} / \Delta
m_{31}^{2}$ and those unitarity violation parameters $s^{2}_{ij}$ (for i = 1,
2, 3 and j = 4, 5, 6) up to the first order are studied in this paper. We
analyse the accuracy of the analytical series expansion formulas in different
regions of L / E. A detailed numerical analysis is also performed, of which the
different effects of the direct and the indirect unitarity violation are
particularly emphasized. We also study in this paper the summed
$\nu^{}_{\alpha} \rightarrow \nu^{}_{e, \nu, \tau}$ probabilities, whose
deviation from the unity provides a definite signal of the unitarity violation.
