_arb_poly_zeta_series, arb_poly_zeta_series
#include <flint/arb_poly.h>void _arb_poly_zeta_series(arb_ptr res, arb_srcptr h, slong hlen, const arb_t a, int deflate, slong len, slong prec)sourcevoid arb_poly_zeta_series(arb_poly_t res, const arb_poly_t s, const arb_t a, int deflate, slong n, slong prec)sourceSet res to the Hurwitz zeta function \zeta(s, a) of the power series s, for a constant a > 0, truncated to length n; a = 1 gives the Riemann zeta function. If a contains a nonpositive number, the result is indeterminate. If deflate is nonzero, \zeta(s, a) + 1/(1 - s) is computed, which is finite at s = 1.
The series of \zeta(s_0 + x, a) is computed by Euler–Maclaurin summation (_acb_poly_zeta_cpx_series) and composed with s - s_0 (Zeta functions, polylogarithms and L-functions). For a = 1 and a constant term with negative midpoint the functional equation is used. With s = 1 + x and deflate set, the result is \sum_{k=0}^{n-1} \frac{(-1)^k}{k!} \gamma_k(a) x^k in terms of the Stieltjes constants \gamma_k(a).
The FLINT team, “_arb_poly_zeta_series, arb_poly_zeta_series (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_zeta_series.html (generated 2026-10-20).
@misc{flint-doc-arb-poly-arb-poly-zeta-series,
author = {{The FLINT team}},
title = {{\_arb\_poly\_zeta\_series, arb\_poly\_zeta\_series (arb\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/arb_poly/_arb_poly_zeta_series.html},
note = {Generated 2026-10-20}
}