Conjecture on the radius of convergence of Fox–Wright expansions

Let ${}_{p}\Psi_q$ denote the Fox–Wright function, and consider the series in equations,, and, each expanded about the relevant point in the variable $1-z$. Radius-of-convergence conjecture. The true radius of convergence of all these series is equal to unity. The value $1/2$ established in the preceding convergence arguments is only a lower bound obtained before interchanging the order of summation; determining the true radius clarifies the analytic behavior of these expansions near the singularity and branch cut.