The asymptotics for eigenvalues of a differential Jacobi-type operator with $\alpha=\frac{1}{2}$ and $\beta=-\frac{1}{2}$

Using the perturbation theory corrections we find the asymptotics for eigenvalues of a differential Jacobi-type operator with $\alpha=\frac{1}{2}$ and $\beta=-\frac{1}{2}$ with coefficient up to sum-converging members.