  We deal with the Sturm--Liouville operator
$Ly=l(y)=-\dfrac{d^2y}{dx^2}+q(x)y,$ with Dirichlet--Neumann boundary
conditions $ y(0)=y'(\pi)=0 $ in the space $L_2[0,\pi]$. We assume that the
potential $q$ is complex-valued and has the form $q(x)=u'(x)$, where $u\in
L_2[0,\pi]$. Here the derivative is treated in the distributional sense. Our
aim is to obtain the detailed asymptotic formulae for eigenvalues and eigen-
and associated functions of the operator $L$.
