FLINT3.7.0-dev
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arb_hypgeom_rising_ui_jet_powsum, arb_hypgeom_rising_ui_jet_bs, arb_hypgeom_rising_ui_jet_rs, arb_hypgeom_rising_ui_jet

Synopsis#include <flint/arb_hypgeom.h>
void arb_hypgeom_rising_ui_jet_powsum(arb_ptr res, const arb_t x, ulong n, slong len, slong prec)source
void arb_hypgeom_rising_ui_jet_bs(arb_ptr res, const arb_t x, ulong n, slong len, slong prec)source
void arb_hypgeom_rising_ui_jet_rs(arb_ptr res, const arb_t x, ulong n, ulong m, slong len, slong prec)source
void arb_hypgeom_rising_ui_jet(arb_ptr res, const arb_t x, ulong n, slong len, slong prec)source

Sets the vector res of length len to the coefficients of the polynomial (x + t)_n = (x+t)(x+t+1)\cdots(x+t+n-1) \in \mathbb{R}[t], truncated to length len if \mathit{len} < n+1 and padded with zeros if \mathit{len} > n+1. The coefficient of t^k is the k-th derivative of (x)_n with respect to x divided by k!.

arb_hypgeom_rising_ui_jet_powsum computes the powers of x and forms the coefficients as integer linear combinations of them; arb_hypgeom_rising_ui_jet_bs uses binary splitting of the product of the linear polynomials x + k + t; arb_hypgeom_rising_ui_jet_rs uses rectangular splitting with block size m (0 chooses it), multiplying the block polynomials as truncated power series. arb_hypgeom_rising_ui_jet chooses: len = 1 is arb_hypgeom_rising_ui_rec, n \le 7 uses the power sums, and otherwise the choice depends on n, len, prec and the bit length of x (binary splitting for \mathit{len} \ge 64, or for n \ge 32 and x with fewer than \mathit{prec}/1024 bits). The output must not overlap x.

Cite this page

The FLINT team, “arb_hypgeom_rising_ui_jet_powsum, arb_hypgeom_rising_ui_jet_bs, arb_hypgeom_rising_ui_jet_rs, arb_hypgeom_rising_ui_jet (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_ui_jet_powsum.html (generated 2026-10-20).