arb_hypgeom_si

Implemented for real arguments: the asymptotic expansion $\operatorname{Si}(z) = \frac{\pi}{2} - \frac{\cos z}{z} f(z) - \frac{\sin z}{z} g(z)$ when it reaches the target accuracy, and otherwise the series $\operatorname{Si}(z) = z\, {}_1F_2(\tfrac12; \tfrac32, \tfrac32; -z^2/4)$ at a working precision increased by the $|z|/\log 2$ bits lost to cancellation. Both are summed with arb_hypgeom_sum_fmpq_arb and arb_hypgeom_sum_fmpq_imag_arb. For inexact $z$ the series is evaluated at the midpoint and the propagated error is bounded with $|\operatorname{Si}'(z)| \le \min(1, 1/|z|)$.