gr_bernpoly_ui, gr_eulerpoly_ui
Synopsis
#include <flint/gr_special.h>Set res to the Bernoulli polynomial B_n(x) or the Euler polynomial E_n(x). These methods are implemented for real and complex balls (arb_bernoulli_poly_ui, acb_bernoulli_poly_ui); other rings return GR_UNABLE.
The ball versions compute E_n(x) = 2 (B_{n+1}(x) - 2^{n+1} B_{n+1}(x/2)) / (n+1), with extra working precision to absorb the cancellation between the two terms for large |x|.
Cite this page
The FLINT team, “gr_bernpoly_ui, gr_eulerpoly_ui (gr_special.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/gr_special/gr_bernpoly_ui.html (generated 2026-10-20).
@misc{flint-doc-gr-special-gr-bernpoly-ui,
author = {{The FLINT team}},
title = {{gr\_bernpoly\_ui, gr\_eulerpoly\_ui (gr\_special.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/gr_special/gr_bernpoly_ui.html},
note = {Generated 2026-10-20}
}