Stokes phenomenon arising in the confluence of the Gauss hypergeometric equation (Q2658243)

This paper studies the connection between the Gauss equation \[z(1-z)y''+(\gamma-(\alpha+\beta+1)z)y'-\alpha\beta y=0\tag{1}\] and, obtained from it by the confluence of two regular singularities, the Kummer equation \[zy''+(\gamma-z)y'-\beta y=0.\tag{2}\] The authors give a thorough description of the merger procedure and show as the (wild) monodromy data of the confilent equation (2) can be obtained as limits of the monodromy data of the original equation (1) using explicit formulae. To overcome difficulties arising on this path, one result by Glutsyuk (see [\textit{A. A. Glutsuk}, J. Dyn. Control Syst. 5, No. 1, 101--135 (1999; Zbl 0949.34076)]) is used. For the entire collection see [Zbl 1459.00016].