Smoothing of Stokes's discontinuity for the generalized Bessel function. II

Abstract

This is a continuation of an earlier paper in which we investigated the superasymptotics and hyperasymptotics of the generalized Bessel function ϕ ( z ) = ∑ l = 0 ∞ z l Γ ( l + 1 ) Γ ( ρ l + β ) . where 0 < φ < X and g may be real or complex. In this paper, we consider the case -1 < φ < 0. The analysis in the two cases is not quite the same. Here we shall see that contributions towards hyperasymptotic expansions not only come from adjacent saddles but also from curves that are not even steepest-descent paths through any saddles.