FLINT3.7.0-dev
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mag_polylog_tail

Synopsis#include <flint/mag.h>
void mag_polylog_tail(mag_t res, const mag_t z, slong s, ulong d, ulong N)source

Sets res to an upper bound for

∑k=N∞zklog⁡d(k)ks.\sum_{k=N}^{\infty} \frac{z^k \log^d(k)}{k^s}.

This is the tail bound used when summing polylogarithms and their derivatives. When ss is real or complex, any integer s′≤Re⁡(s)s' \le \operatorname{Re}(s) can be substituted. The derivation is described in Zeta functions, polylogarithms and L-functions.

Cite this page

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