Asymptotic properties of the solutions of a differential equation appearing in QCD

Abstract

We establish the asymptotic behaviour of the ratio $h^{\prime }(0)/h(0)$ for $\lambda \to \infty$, where $h(r)$ is a solution, vanishing at infinity, of the differential equation $h^{\prime \prime }(r)=i\lambda \omega (r)h(r)$ on the domain $0\le r<\infty$ and $\omega (r)=(1-\sqrt{r}{K}_1(\sqrt{r}))/r$. Some results are valid for more general $\omega$'s.

6 pages, latex