acb_hypgeom_bessel_j

For $|z| < 8$ the function sums the convergent series. Otherwise it uses the asymptotic expansion if $|z| \ge 2^{64}$ or $2|z| \ge \mathit{prec}$, and the convergent series otherwise, with the working precision increased by an estimate $(|z| - |\operatorname{Im} z|)/\log 2$ of the cancellation (no increase when the terms have equal signs or $\nu > |z|^2/4$). For inexact input with integer $\nu$ the series is evaluated at the midpoint and the propagated error is bounded with acb_hypgeom_bessel_j_deriv_bound. If the enclosure has less than one bit of accuracy, it is intersected with a direct bound for $|J_\nu(z)|$.