_arb_hypgeom_rising_coeffs_1, _arb_hypgeom_rising_coeffs_2, _arb_hypgeom_rising_coeffs_fmpz
#include <flint/arb_hypgeom.h>Sets c_0, \ldots, c_{n-1} to the coefficients of the monic polynomial (X+k)_n = X^n + c_{n-1} X^{n-1} + \cdots + c_0 (the leading 1 is not stored). Requires n \ge 2 and raises an exception otherwise.
The 1 version stores each coefficient in one word and the 2 version in two words (low word first, so c must have room for 2n words); neither checks for overflow, and the caller must ensure that the coefficients fit, for example by checking that n \lceil\log_2(k+n)\rceil is at most one or two word sizes. The fmpz version has no restriction; it uses the quadratic recurrence (X+k)_{i+1} = (X+k)_i (X + k + i), which is not asymptotically fast. These are the block polynomials of rectangular splitting in arb_hypgeom_rising_ui_rs and arb_hypgeom_rising_ui_jet_rs.
The FLINT team, “_arb_hypgeom_rising_coeffs_1, _arb_hypgeom_rising_coeffs_2, _arb_hypgeom_rising_coeffs_fmpz (arb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_hypgeom/_arb_hypgeom_rising_coeffs_1.html (generated 2026-10-20).
@misc{flint-doc-arb-hypgeom-arb-hypgeom-rising-coeffs-1,
author = {{The FLINT team}},
title = {{\_arb\_hypgeom\_rising\_coeffs\_1, \_arb\_hypgeom\_rising\_coeffs\_2, \_arb\_hypgeom\_rising\_coeffs\_fmpz (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_rising_coeffs_1.html},
note = {Generated 2026-10-20}
}