C++ (Cpp) _acb_hypgeom_m_1f1 Examples

Example #1

File: m.c Project: argriffing/arb

void
acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec)
{
    if (arf_sgn(arb_midref(acb_realref(z))) >= 0
        || (acb_is_int(a) && arb_is_nonpositive(acb_realref(a))))
    {
        _acb_hypgeom_m_1f1(res, a, b, z, regularized, prec, prec, 0);
    }
    else
    {
        _acb_hypgeom_m_1f1(res, a, b, z, regularized, prec, prec, 1);
    }
}

Example #2

File: m.c Project: UBunt14/SourceOfBasicLibraries

void
acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, long prec)
{
    acb_t t;

    if (regularized)
    {
        acb_init(t);
        acb_rgamma(t, b, prec);
    }

    if (arf_sgn(arb_midref(acb_realref(z))) >= 0
        || (acb_is_int(a) && arb_is_nonpositive(acb_realref(a))))
    {
        _acb_hypgeom_m_1f1(res, a, b, z, prec);
    }
    else
    {
        /* Kummer's transformation */
        acb_t u, v;
        acb_init(u);
        acb_init(v);

        acb_sub(u, b, a, prec);
        acb_neg(v, z);

        _acb_hypgeom_m_1f1(u, u, b, v, prec);
        acb_exp(v, z, prec);
        acb_mul(res, u, v, prec);

        acb_clear(u);
        acb_clear(v);
    }

    if (regularized)
    {
        acb_mul(res, res, t, prec);
        acb_clear(t);
    }
}

Example #3

File: m.c Project: argriffing/arb

void
acb_hypgeom_m(acb_t res, const acb_t a, const acb_t b, const acb_t z, int regularized, slong prec)
{
    int asymp, kummer;
    slong wp;

    acb_hypgeom_m_choose(&asymp, &kummer, &wp, a, b, z, regularized, prec);

    if (asymp)
    {
        acb_hypgeom_m_asymp(res, a, b, z, regularized, wp);
    }
    else
    {
        _acb_hypgeom_m_1f1(res, a, b, z, regularized, wp, FLINT_MIN(wp, prec), kummer);
    }

    acb_set_round(res, res, prec);
}

Example #4

File: m.c Project: argriffing/arb

void
_acb_hypgeom_m_1f1(acb_t res, const acb_t a, const acb_t b, const acb_t z,
    int regularized, slong prec, slong gamma_prec, int kummer)
{
    if (regularized)
    {
        /* Remove singularity */
        if (acb_is_int(b) && arb_is_nonpositive(acb_realref(b)) &&
            arf_cmpabs_2exp_si(arb_midref(acb_realref(b)), 30) < 0)
        {
            acb_t c, d, t, u;
            slong n;

            n = arf_get_si(arb_midref(acb_realref(b)), ARF_RND_DOWN);

            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, gamma_prec, kummer);

            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_t t;
            acb_init(t);
            acb_rgamma(t, b, gamma_prec);
            _acb_hypgeom_m_1f1(res, a, b, z, 0, prec, gamma_prec, kummer);
            acb_mul(res, res, t, prec);
            acb_clear(t);
        }
        return;
    }

    /* Kummer's transformation */
    if (kummer)
    {
        acb_t u, v;
        acb_init(u);
        acb_init(v);

        acb_sub(u, b, a, prec);
        acb_neg(v, z);

        _acb_hypgeom_m_1f1(u, u, b, v, regularized, prec, gamma_prec, 0);
        acb_exp(v, z, prec);
        acb_mul(res, u, v, prec);

        acb_clear(u);
        acb_clear(v);
        return;
    }

    if (acb_is_one(a))
    {
        acb_hypgeom_pfq_direct(res, NULL, 0, b, 1, z, -1, prec);
    }
    else
    {
        acb_struct c[3];
        c[0] = *a;
        c[1] = *b;

        acb_init(c + 2);
        acb_one(c + 2);

        acb_hypgeom_pfq_direct(res, c, 1, c + 1, 2, z, -1, prec);

        acb_clear(c + 2);
    }
}