FLINT3.7.0-dev
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acb_hypgeom_u

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_u(acb_t res, const acb_t a, const acb_t b, const acb_t z, slong prec)source

Sets res to U(a,b,z)U(a,b,z).

For small nonpositive integer aa, UU is a polynomial in zz computed by its three-term recurrence (with binary splitting for −a≥20-a \ge 20). If aa or a−b+1a - 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|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.

Cite this page

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 2026-11-02).