Higher-order asymptotic approximations to the eigenvalues of the Sturm-Liouville problem in one turning point case (Q1305234)

The author obtains higher-order asymptotic approximations to the eigenvalues of the Sturm-Liouville problem \[ y''- q(x)y= \lambda^2f(x),\quad a\leq x\leq b,\quad y(a)= y(b)= 0, \] where for some point \(x_0\in (a,b)\): 1) \(f(x_0)= 0\), 2) \(f(x_0)=(x- x_0)^{-1}\), 3) \(q\) is continuously differentiable.