  The Fox-Wright function is a further extension of the generalized
hypergeometric function obtained by introducing arbitrary positive scaling
factors into the arguments of the gamma functions in the summand. Its
importance comes mostly from its role in fractional calculus although other
interesting applications also exist. If the sums of the scaling factors in the
top and bottom parameters are equal, the series defining the Fox-Wright
function has a finite non-zero radius of convergence. It was demonstrated by
Braaksma in 1964 that the Fox-Wright function can then be extended to a
holomorphic function in the complex plane cut along a ray from the positive
point on the boundary of the disk of convergence to the point at infinity. In
this paper we study the behavior of the Fox-Wright function in the neighborhood
of this positive singular point. Under certain restrictions we give a
convergent expansion with recursively computed coefficients completely
characterizing this behavior. We further compute the jump and the average value
of the Fox-Wright function on the banks of the branch cut.
