acb_hypgeom_u
#include <flint/acb_hypgeom.h>For small nonpositive integer a, U is a polynomial in z computed by its three-term recurrence (with binary splitting for -a \ge 20). If a or a - b + 1 is a nonpositive integer, or acb_hypgeom_u_use_asymp returns true, the (terminating or convergent enough) asymptotic series is used. Otherwise the function compares the expected accuracy of the asymptotic series with that of acb_hypgeom_u_1f1, whose cancellation it estimates as |z|/\log 2 bits, and chooses the working precision. As with acb_hypgeom_m, real arguments with an inaccurate result are retried with arb_hypgeom_u_integration.
The FLINT team, “acb_hypgeom_u (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_u.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-u,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_u (acb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_u.html},
note = {Generated 2026-10-20}
}