We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, pΨq(z) for large |z| that have not been considered in the existing theory. Our interest is principally with those functions of this class that possess either a finite algebraic expansion or no such expansion and with parameter values that produce exponentially small expansions in the neighbourhood of the negative real z axis. Numerical examples are presented to demonstrate the presence of these exponentially small expansions.
Paris, R. B. (2010). Exponentially small expansions in the asymptotics of the Wright function. Journal of Computational and Applied Mathematics, 234(2), 488-504. https://doi.org/10.1016/j.cam.2009.12.040