arb_hypgeom_si
#include <flint/arb_hypgeom.h>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|).
The FLINT team, “arb_hypgeom_si (arb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_hypgeom/arb_hypgeom_si.html (generated 2026-10-20).
@misc{flint-doc-arb-hypgeom-arb-hypgeom-si,
author = {{The FLINT team}},
title = {{arb\_hypgeom\_si (arb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb_hypgeom/arb_hypgeom_si.html},
note = {Generated 2026-10-20}
}