FLINT3.7.0-dev

acb_hypgeom_dilog_transform

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_dilog_transform(acb_t res, const acb_t z, int algorithm, slong prec)source

Sets res to Li⁡2(z)\operatorname{Li}_2(z) computed by one of the transformations 1/z1/z, 1−z1-z, z/(z−1)z/(z-1), 1/(1−z)1/(1-z), selected by algorithm from 1 to 4, followed by acb_hypgeom_dilog_zero at the transformed argument. For algorithm between 5 and 7, it instead starts from the respective point ±i\pm i, (1±i)/2(1\pm i)/2 or 1±i1 \pm i (with the sign of the imaginary part of zz), where Li⁡2\operatorname{Li}_2 has a closed form in terms of π\pi, log⁡2\log 2 and Catalan's constant, and continues to zz with the bit-burst method; these require that the imaginary part of zz does not contain 0. The result is indeterminate if the transformation is not valid on the whole input ball.

Cite this page

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