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

arb_hypgeom_rising_ui_jet_powsum computes the powers of xx 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+tx + k + t; arb_hypgeom_rising_ui_jet_rs uses rectangular splitting with block size mm (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≤7n \le 7 uses the power sums, and otherwise the choice depends on nn, len, prec and the bit length of xx (binary splitting for len≥64\mathit{len} \ge 64, or for n≥32n \ge 32 and xx with fewer than prec/1024\mathit{prec}/1024 bits). The output must not overlap xx.

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 2026-11-02).