FLINT3.7.0-dev
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acb_hypgeom_chi_asymp, acb_hypgeom_chi_2f3, acb_hypgeom_chi

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_chi_asymp(acb_t res, const acb_t z, slong prec)source
void acb_hypgeom_chi_2f3(acb_t res, const acb_t z, slong prec)source
void acb_hypgeom_chi(acb_t res, const acb_t z, slong prec)source

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

Chi⁡(z)=−12[ezU(1,1,−z)+e−zU(1,1,z)+log⁡(−z)−log⁡(z)],\operatorname{Chi}(z) = -\frac{1}{2} \left[ e^{z} U(1,1,-z) + e^{-z} U(1,1,z) + \log(-z) - \log(z) \right],
Chi⁡(z)=z24 2F3(1,1;2,2,32;z24)+log⁡(z)+γ,\operatorname{Chi}(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.

Cite this page

The FLINT team, “acb_hypgeom_chi_asymp, acb_hypgeom_chi_2f3, acb_hypgeom_chi (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_chi_asymp.html (generated 2026-11-02).