acb_dirichlet_eta
Synopsis
#include <flint/acb_dirichlet.h>Sets res to the Dirichlet eta function \eta(s) = \sum_{k=1}^{\infty} (-1)^{k+1} k^{-s} = (1-2^{1-s}) \zeta(s) (the alternating character is not a Dirichlet character). The removable singularity at s = 1, where \eta(1) = \log 2, is handled.
Cite this page
The FLINT team, “acb_dirichlet_eta (acb_dirichlet.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_eta.html (generated 2026-10-20).
@misc{flint-doc-acb-dirichlet-acb-dirichlet-eta,
author = {{The FLINT team}},
title = {{acb\_dirichlet\_eta (acb\_dirichlet.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_dirichlet/acb_dirichlet_eta.html},
note = {Generated 2026-10-20}
}