FLINT3.7.0-dev
/

_arb_hypgeom_rising_coeffs_1, _arb_hypgeom_rising_coeffs_2, _arb_hypgeom_rising_coeffs_fmpz

Synopsis#include <flint/arb_hypgeom.h>
void _arb_hypgeom_rising_coeffs_1(ulong * c, ulong k, slong n)source
void _arb_hypgeom_rising_coeffs_2(ulong * c, ulong k, slong n)source
void _arb_hypgeom_rising_coeffs_fmpz(fmpz * c, ulong k, slong n)source

Sets c0,…,cn−1c_0, \ldots, c_{n-1} to the coefficients of the monic polynomial (X+k)n=Xn+cn−1Xn−1+⋯+c0(X+k)_n = X^n + c_{n-1} X^{n-1} + \cdots + c_0 (the leading 1 is not stored). Requires n≥2n \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 cc must have room for 2n2n words); neither checks for overflow, and the caller must ensure that the coefficients fit, for example by checking that n⌈log⁡2(k+n)⌉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)(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.

Cite this page

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 2026-11-02).