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We deal with the Sturm--Liouville operator$Ly=l(y)=-\dfrac{d^2y}{dx^2}+q(x)y,$ with Dirichlet--Neumann boundaryconditions $ y(0)=y'(\pi)=0 $ in the space $L_2[0,\pi]$. We assume that thepotential $q$ is complex-valued and has the form $q(x)=u'(x)$, where $u\inL_2[0,\pi]$. Here the derivative is treated in the distributional sense. Ouraim is to obtain the detailed asymptotic formulae for eigenvalues and eigen-and associated functions of the operator $L$.

Asymptotic formulae for eigenvalues and eigenfunctions of  Sturm--Liouville operators with potentials---distributions.  Dirichlet--Neumann boundary conditions