  In this paper we study the Gauss and Kummer hypergeometric equations in
depth. In particular, we focus on the confluence of two regular singularities
of the Gauss hypergeometric equation to produce the Kummer hypergeometric
equation with an irregular singularity at infinity. We show how to pass from
solutions with power-like behaviour which are analytic in disks, to solutions
with exponential behaviour which are analytic in sectors and have divergent
asymptotics. We explicitly calculate the Stokes matrices of the confluent
system in terms of the monodromy data, specifically the connection matrices, of
the original system around the merging singularities.
