void
acb_hypgeom_2f1_series_direct(acb_poly_t res,
const acb_poly_t a, const acb_poly_t b,
const acb_poly_t c, const acb_poly_t z, int regularized, slong len, slong prec)
{
acb_poly_struct aa[4];
aa[0] = *a;
aa[1] = *b;
aa[2] = *c;
acb_poly_init(&aa[3]);
acb_poly_one(&aa[3]);
acb_hypgeom_pfq_series_direct(res, aa, 2, aa + 2, 2, z,
regularized, -1, len, prec);
acb_poly_clear(&aa[3]);
}
void
acb_hypgeom_bessel_k_0f1_series(acb_poly_t res,
const acb_poly_t nu, const acb_poly_t z,
slong len, slong prec)
{
acb_poly_t s, u, A, B;
acb_poly_struct b[2];
arb_t c;
slong wlen;
int singular;
acb_poly_init(s);
acb_poly_init(u);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(b + 0);
acb_poly_init(b + 1);
arb_init(c);
singular = (nu->length == 0) || acb_is_int(nu->coeffs);
wlen = len + (singular != 0);
/* A = (z/2)^nu, B = 1/A */
acb_poly_scalar_mul_2exp_si(A, z, -1);
acb_poly_pow_series(A, A, nu, wlen, prec);
acb_poly_inv_series(B, A, wlen, prec);
acb_poly_mullow(u, z, z, wlen, prec);
acb_poly_scalar_mul_2exp_si(u, u, -2);
acb_poly_one(b + 1);
acb_poly_add_si(b + 0, nu, 1, prec);
acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec);
acb_poly_mullow(A, A, s, wlen, prec);
acb_poly_add_si(b + 0, nu, -1, prec);
acb_poly_neg(b + 0, b + 0);
acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec);
acb_poly_mullow(B, B, s, wlen, prec);
acb_poly_sub(A, B, A, prec);
acb_poly_scalar_mul_2exp_si(A, A, -1);
/* multiply by pi csc(pi nu) */
acb_poly_sin_pi_series(B, nu, wlen, prec);
if (singular)
{
acb_poly_shift_right(A, A, 1);
acb_poly_shift_right(B, B, 1);
}
acb_poly_div_series(res, A, B, len, prec);
arb_const_pi(c, prec);
_acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec);
acb_poly_clear(s);
acb_poly_clear(u);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(b + 0);
acb_poly_clear(b + 1);
arb_clear(c);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("pfq_series_direct....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
acb_poly_struct a[4], b[4];
acb_poly_t z, s1, s2;
slong i, p, q, len1, len2, n1, n2, prec1, prec2;
int regularized;
p = n_randint(state, 3);
q = n_randint(state, 3);
len1 = n_randint(state, 8);
len2 = n_randint(state, 8);
prec1 = 2 + n_randint(state, 400);
prec2 = 2 + n_randint(state, 400);
if (n_randint(state, 2))
n1 = -1;
else
n1 = n_randint(state, 50);
if (n_randint(state, 2))
n2 = -1;
else
n2 = n_randint(state, 50);
regularized = n_randint(state, 2);
acb_poly_init(z);
acb_poly_init(s1);
acb_poly_init(s2);
for (i = 0; i < p; i++)
acb_poly_init(a + i);
for (i = 0; i < q; i++)
acb_poly_init(b + i);
acb_poly_randtest(z, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 10);
for (i = 0; i < p; i++)
acb_poly_randtest(a + i, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 3);
for (i = 0; i < q; i++)
acb_poly_randtest(b + i, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 3);
acb_hypgeom_pfq_series_direct(s1, a, p, b, q, z, regularized, n1, len1, prec1);
acb_hypgeom_pfq_series_direct(s2, a, p, b, q, z, regularized, n2, len2, prec2);
acb_poly_truncate(s1, FLINT_MIN(len1, len2));
acb_poly_truncate(s2, FLINT_MIN(len1, len2));
if (!acb_poly_overlaps(s1, s2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %wd\n", iter);
flint_printf("n1 = %wd, n2 = %wd prec1 = %wd, prec2 = %wd\n\n", n1, n2, prec1, prec2);
flint_printf("p = %wd, q = %wd\n\n", p, q);
flint_printf("z = "); acb_poly_printd(z, 15); flint_printf("\n\n");
for (i = 0; i < p; i++)
{
flint_printf("a[%wd] = ", i); acb_poly_printd(a + i, 15); flint_printf("\n\n");
}
for (i = 0; i < q; i++)
{
flint_printf("b[%wd] = ", i); acb_poly_printd(b + i, 15); flint_printf("\n\n");
}
flint_printf("s1 = "); acb_poly_printd(s1, 15); flint_printf("\n\n");
flint_printf("s2 = "); acb_poly_printd(s2, 15); flint_printf("\n\n");
acb_poly_sub(s1, s1, s2, prec1);
flint_printf("diff = "); acb_poly_printd(s1, 15); flint_printf("\n\n");
abort();
}
acb_poly_clear(z);
acb_poly_clear(s1);
acb_poly_clear(s2);
for (i = 0; i < p; i++)
acb_poly_clear(a + i);
for (i = 0; i < q; i++)
acb_poly_clear(b + i);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
acb_hypgeom_u_1f1_series(acb_poly_t res,
const acb_poly_t a, const acb_poly_t b, const acb_poly_t z,
long len, long prec)
{
acb_poly_t s, u, A, B;
acb_poly_struct aa[3];
arb_t c;
long wlen;
int singular;
acb_poly_init(s);
acb_poly_init(u);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(aa + 0);
acb_poly_init(aa + 1);
acb_poly_init(aa + 2);
arb_init(c);
singular = (b->length == 0) || acb_is_int(b->coeffs);
wlen = len + (singular != 0);
/* A = rgamma(a-b+1) * 1F~1(a,b,z) */
acb_poly_sub(u, a, b, prec);
acb_poly_add_si(u, u, 1, prec);
acb_poly_rgamma_series(A, u, wlen, prec);
/* todo: handle a = 1 efficiently */
acb_poly_set(aa, a);
acb_poly_set(aa + 1, b);
acb_poly_one(aa + 2);
acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec);
acb_poly_mullow(A, A, s, wlen, prec);
/* B = rgamma(a) * 1F~1(a-b+1,2-b,z) * z^(1-b) */
acb_poly_set(aa, u);
acb_poly_add_si(aa + 1, b, -2, prec);
acb_poly_neg(aa + 1, aa + 1);
acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec);
acb_poly_rgamma_series(B, a, wlen, prec);
acb_poly_mullow(B, B, s, wlen, prec);
acb_poly_add_si(u, b, -1, prec);
acb_poly_neg(u, u);
acb_poly_pow_series(s, z, u, wlen, prec);
acb_poly_mullow(B, B, s, wlen, prec);
acb_poly_sub(A, A, B, prec);
/* multiply by pi csc(pi b) */
acb_poly_sin_pi_series(B, b, wlen, prec);
if (singular)
{
acb_poly_shift_right(A, A, 1);
acb_poly_shift_right(B, B, 1);
}
acb_poly_div_series(res, A, B, len, prec);
arb_const_pi(c, prec);
_acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec);
acb_poly_clear(s);
acb_poly_clear(u);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(aa + 0);
acb_poly_clear(aa + 1);
acb_poly_clear(aa + 2);
arb_clear(c);
}
