FLINT3.7.0-dev
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acb_hypgeom_ci_asymp, acb_hypgeom_ci_2f3, acb_hypgeom_ci

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_ci_asymp(acb_t res, const acb_t z, slong prec)source
void acb_hypgeom_ci_2f3(acb_t res, const acb_t z, slong prec)source
void acb_hypgeom_ci(acb_t res, const acb_t z, slong prec)source

Sets res to the cosine integral Ci⁡(z)\operatorname{Ci}(z), computed respectively from

Ci⁡(z)=log⁡(z)−12[eizU(1,1,−iz)+e−izU(1,1,iz)+log⁡(−iz)+log⁡(iz)],\operatorname{Ci}(z) = \log(z) - \frac{1}{2} \left[ e^{iz} U(1,1,-iz) + e^{-iz} U(1,1,iz) + \log(-iz) + \log(iz) \right],
Ci⁡(z)=−z24 2F3(1,1;2,2,32;−z24)+log⁡(z)+γ,\operatorname{Ci}(z) = -\tfrac{z^2}{4}\, {}_2F_3(1, 1; 2, 2, \tfrac{3}{2}; -\tfrac{z^2}{4}) + \log(z) + \gamma,

or by an automatic choice. Positive real input is passed to arb_hypgeom_ci.

Cite this page

The FLINT team, “acb_hypgeom_ci_asymp, acb_hypgeom_ci_2f3, acb_hypgeom_ci (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_ci_asymp.html (generated 2026-11-02).