  We present closed-form analytic solutions to non-secular Bloch-Redfield
master equations for quantum dynamics of a V-type system driven by weak
coupling to a thermal bath. We focus on noise-induced Fano coherences among the
excited states induced by incoherent driving of the V-system initially in the
ground state. For suddenly turned-on incoherent driving, the time evolution of
the coherences is determined by the damping parameter
$\zeta=\frac{1}{2}(\gamma_1+\gamma_2)/\Delta_p$, where $\gamma_i$ are the
radiative decay rates of the excited levels $i=1,2$, and
$\Delta_p=\sqrt{\Delta^2 + (1-p^2)\gamma_1\gamma_2}$ depends on the
excited-state level splitting $\Delta>0$ and the angle between the transition
dipole moments in the energy basis. The coherences oscillate as a function of
time in the underdamped limit ($\zeta\gg1$), approach a long-lived quasi-steady
state in the overdamped limit ($\zeta\ll 1$), and display an intermediate
behavior at critical damping ($\zeta= 1$). The sudden incoherent turn-on
generates a mixture of excited eigenstates $|e_1\rangle$ and $|e_2\rangle$ and
their in-phase coherent superposition $|\phi_+\rangle =
\frac{1}{\sqrt{2\bar{r}}}(\sqrt{r_1} |e_1\rangle + \sqrt{r_2}|e_2\rangle)$,
which is remarkably long-lived in the overdamped limit (where $r_1$ and $r_2$
are the incoherent pumping rates). Formation of this coherent superposition
{\it enhances} the decay rate from the excited states to the ground state. In
the strongly asymmetric V-system where the coupling strengths between the
ground state and the excited states differ significantly, we identify
additional asymptotic quasistationary coherences, which arise due to slow
equilibration of one of the excited states. Finally, we demonstrate that
noise-induced Fano coherences are maximized with respect to populations when
$r_1=r_2$ and the transition dipole moments are fully aligned.
