Coalescence of two regular singularities into one regular singularity for the linear ordinary differential equation (Q1868359)

The author studies the process of coalescing of two regular singular points of the second-order linear ODE \[ z(z+ \varepsilon) \frac {d^2}{dz ^2} w(z) + P (z, \varepsilon)\frac d {dz}w(z) + Q (z, \varepsilon) w(z) = 0, \] as \(\varepsilon\) goes to infinity, into a single singularity. This problem is discussed in terms of connection matrices and solutions to the corresponding equations.