FLINT3.7.0-dev
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acb_hypgeom_si_asymp, acb_hypgeom_si_1f2, acb_hypgeom_si

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_si_asymp(acb_t res, const acb_t z, slong prec)source
void acb_hypgeom_si_1f2(acb_t res, const acb_t z, slong prec)source
void acb_hypgeom_si(acb_t res, const acb_t z, slong prec)source

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

Si⁡(z)=i2[eizU(1,1,−iz)−e−izU(1,1,iz)+log⁡(−iz)−log⁡(iz)],\operatorname{Si}(z) = \frac{i}{2} \left[ e^{iz} U(1,1,-iz) - e^{-iz} U(1,1,iz) + \log(-iz) - \log(iz) \right],
Si⁡(z)=z 1F2(12;32,32;−z24),\operatorname{Si}(z) = z\, {}_1F_2(\tfrac{1}{2}; \tfrac{3}{2}, \tfrac{3}{2}; -\tfrac{z^2}{4}),

or by an automatic choice. Real input is passed to arb_hypgeom_si.

Cite this page

The FLINT team, “acb_hypgeom_si_asymp, acb_hypgeom_si_1f2, acb_hypgeom_si (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_si_asymp.html (generated 2026-11-02).