_acb_poly_lambertw_series, acb_poly_lambertw_series
Synopsis
#include <flint/acb_poly.h>void _acb_poly_lambertw_series(acb_ptr res, acb_srcptr z, slong zlen, const fmpz_t k, int flags, slong len, slong prec)sourcevoid acb_poly_lambertw_series(acb_poly_t res, const acb_poly_t z, const fmpz_t k, int flags, slong len, slong prec)sourceSet res to branch k of the Lambert W function of the power series z, truncated to length len. The value at the constant term is computed by acb_lambertw with the same k and flags (which select the branch cut conventions, see there) [Joh2017b], and the remaining coefficients by Newton iteration on w e^w = z. The underscore version allows aliasing.
References#
- [Joh2017b] F. Johansson, "Computing the Lambert W function in arbitrary-precision complex interval arithmetic", preprint (2017), https://arxiv.org/abs/1705.03266
Cite this page
The FLINT team, “_acb_poly_lambertw_series, acb_poly_lambertw_series (acb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_poly/_acb_poly_lambertw_series.html (generated 2026-10-20).
@misc{flint-doc-acb-poly-acb-poly-lambertw-series,
author = {{The FLINT team}},
title = {{\_acb\_poly\_lambertw\_series, acb\_poly\_lambertw\_series (acb\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_poly/_acb_poly_lambertw_series.html},
note = {Generated 2026-10-20}
}