Study of the Equation of Partial Waves with Rapidly Oscillating Potential

In this paper, we consider the differential equation of partial waves $\psi''(x)+[k^2-(\lambda^2-1/4)/x^2-V(x)]\psi(x)=0$ and the corresponding integral equations. We obtain estimates for the solutions of this differential equation with boundary conditions for $x=0$ and $x=\infty$. The analitycity domains for the wave functions are established.