void
acb_hypgeom_u(acb_t res, const acb_t a, const acb_t b, const acb_t z, long prec)
{
acb_t t;
acb_init(t);
acb_sub(t, a, b, prec);
acb_add_ui(t, t, 1, prec);
if ((acb_is_int(a) && arf_sgn(arb_midref(acb_realref(a))) <= 0) ||
(acb_is_int(t) && arf_sgn(arb_midref(acb_realref(t))) <= 0) ||
acb_hypgeom_u_use_asymp(z, prec))
{
acb_neg(t, a);
acb_pow(t, z, t, prec);
acb_hypgeom_u_asymp(res, a, b, z, -1, prec);
acb_mul(res, res, t, prec);
}
else
{
acb_hypgeom_u_1f1(res, a, b, z, prec);
}
acb_clear(t);
}
void
acb_hypgeom_ci(acb_t res, const acb_t z, slong prec)
{
if (acb_hypgeom_u_use_asymp(z, prec))
acb_hypgeom_ci_asymp(res, z, prec);
else
acb_hypgeom_ci_2f3(res, z, prec);
}
void
acb_hypgeom_m(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, long prec)
{
long m = LONG_MAX;
long n = LONG_MAX;
if (acb_is_int(a) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(a)), 30) < 0)
{
m = arf_get_si(arb_midref(acb_realref(a)), ARF_RND_DOWN);
}
if (acb_is_int(b) &&
arf_cmpabs_2exp_si(arb_midref(acb_realref(b)), 30) < 0)
{
n = arf_get_si(arb_midref(acb_realref(b)), ARF_RND_DOWN);
}
/* terminating */
if (m <= 0 && m < n && m > -10 * prec && (n > 0 || !regularized))
{
acb_hypgeom_m_1f1(res, a, b, z, regularized, prec);
return;
}
/* large */
if (acb_hypgeom_u_use_asymp(z, prec))
{
acb_hypgeom_m_asymp(res, a, b, z, regularized, prec);
return;
}
/* remove singularity */
if (n <= 0 && n > -10 * prec && regularized)
{
acb_t c, d, t, u;
acb_init(c);
acb_init(d);
acb_init(t);
acb_init(u);
acb_sub(c, a, b, prec);
acb_add_ui(c, c, 1, prec);
acb_neg(d, b);
acb_add_ui(d, d, 2, prec);
acb_hypgeom_m_1f1(t, c, d, z, 0, prec);
acb_pow_ui(u, z, 1 - n, prec);
acb_mul(t, t, u, prec);
acb_rising_ui(u, a, 1 - n, prec);
acb_mul(t, t, u, prec);
arb_fac_ui(acb_realref(u), 1 - n, prec);
acb_div_arb(res, t, acb_realref(u), prec);
acb_clear(c);
acb_clear(d);
acb_clear(t);
acb_clear(u);
}
else
{
acb_hypgeom_m_1f1(res, a, b, z, regularized, prec);
}
}
