FLINT3.7.0-dev
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acb_hypgeom_pfq_direct

Synopsis#include <flint/acb_hypgeom.h>
void acb_hypgeom_pfq_direct(acb_t res, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong n, slong prec)source

Sets res to

pfq(z)=∑k=0∞T(k)=∑k=0n−1T(k)+ε,{}_pf_{q}(z) = \sum_{k=0}^{\infty} T(k) = \sum_{k=0}^{n-1} T(k) + \varepsilon,

computed directly from the series with acb_hypgeom_pfq_sum and a rigorous bound for the truncation error ε\varepsilon from acb_hypgeom_pfq_bound_factor. If n<0n < 0, the number of terms is chosen with acb_hypgeom_pfq_choose_n. If T(n)T(n) is exactly zero (a terminating series), no error is added. For real input the error is added to the real part only.

Cite this page

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