Degeneration of Heun equation solutions under fusion of singularities (Q1280394)

Let \[ {d^2y\over dz^2}+ \Biggl({\gamma\over z}+{\delta\over z-1}+{\varepsilon\over z- a}\Biggr) {dy\over dz}+ {\alpha\beta z-q\over z(z- 1)(z- a)} y= 0\tag{1} \] be the Heun equation and \[ {d^2y\over dz^2}+ \Biggl({\gamma\over z}+ {\delta\over z- 1}+ p\Biggr) {dy\over dz}+ {\alpha pz- q\over z(z-1)} y= 0\tag{2} \] the degenerate Heun equation. The author shows that there is a limiting transition from equation (1) to equation (2) such that the characteristics of the singular points are unchanged and the eigenfunctions of (1) are mapped into the eigenfunctions of (2).