FLINT3.7.0-dev
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acb_hypgeom_coulomb

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_coulomb(acb_t F, acb_t G, acb_t Hpos, acb_t Hneg, const acb_t l, const acb_t eta, const acb_t z, slong prec)source

Sets F, G, Hpos, Hneg to the respective Coulomb wave functions. Any of the outputs may be NULL.

All four are computed from U(1+ℓ±iη,2ℓ+2,∓2iz)U(1 + \ell \pm i\eta, 2\ell + 2, \mp 2iz) (by the asymptotic expansion when ∣z∣|z| is large, by acb_hypgeom_u otherwise) and the log-gamma values log⁡Γ(1+ℓ±iη)\log\Gamma(1 + \ell \pm i\eta), with formulas chosen according to the sign of Re⁡z\operatorname{Re} z and Im⁡z\operatorname{Im} z so that each output is continuous across the real axis except on the branch cut.

Cite this page

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