FLINT3.7.0-dev
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_acb_poly_polylog_cpx_small, _acb_poly_polylog_cpx_zeta, _acb_poly_polylog_cpx

Synopsis#include <flint/acb_poly.h>
void _acb_poly_polylog_cpx_small(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec)source
void _acb_poly_polylog_cpx_zeta(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec)source
void _acb_poly_polylog_cpx(acb_ptr w, const acb_t s, const acb_t z, slong len, slong prec)source

Set {w, len} to the Taylor series in xx of the polylogarithm Li⁡s+x(z)\operatorname{Li}_{s+x}(z) for complex constants ss and zz; len must be positive and w must not alias s or z. The small version sums the power series in zz (for ∣z∣<1|z| < 1), the zeta version writes the polylogarithm as a combination of two Hurwitz zeta functions, and the default uses the small version for ∣z∣<1/2|z| < 1/2 and the zeta version otherwise (and acb_hypgeom_dilog for s=2s = 2 and length 1) (Zeta functions, polylogarithms and L-functions).

Cite this page

The FLINT team, “_acb_poly_polylog_cpx_small, _acb_poly_polylog_cpx_zeta, _acb_poly_polylog_cpx (acb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_poly/_acb_poly_polylog_cpx_small.html (generated 2026-11-02).