int
bessel(acb_ptr out, const acb_t inp, void * params, long order, long prec)
{
acb_ptr t;
acb_t z;
ulong n;
t = _acb_vec_init(order);
acb_init(z);
acb_set(t, inp);
if (order > 1)
acb_one(t + 1);
n = 10;
arb_set_si(acb_realref(z), 20);
arb_set_si(acb_imagref(z), 10);
/* z sin(t) */
_acb_poly_sin_series(out, t, FLINT_MIN(2, order), order, prec);
_acb_vec_scalar_mul(out, out, order, z, prec);
/* t n */
_acb_vec_scalar_mul_ui(t, t, FLINT_MIN(2, order), n, prec);
_acb_poly_sub(out, t, FLINT_MIN(2, order), out, order, prec);
_acb_poly_cos_series(out, out, order, order, prec);
_acb_vec_clear(t, order);
acb_clear(z);
return 0;
}
int
sinx(acb_ptr out, const acb_t inp, void * params, long order, long prec)
{
int xlen = FLINT_MIN(2, order);
acb_set(out, inp);
if (xlen > 1)
acb_one(out + 1);
_acb_poly_sin_series(out, out, xlen, order, prec);
return 0;
}
int
elliptic(acb_ptr out, const acb_t inp, void * params, long order, long prec)
{
acb_ptr t;
t = _acb_vec_init(order);
acb_set(t, inp);
if (order > 1)
acb_one(t + 1);
_acb_poly_sin_series(t, t, FLINT_MIN(2, order), order, prec);
_acb_poly_mullow(out, t, order, t, order, order, prec);
_acb_vec_scalar_mul_2exp_si(t, out, order, -1);
acb_sub_ui(t, t, 1, prec);
_acb_vec_neg(t, t, order);
_acb_poly_rsqrt_series(out, t, order, order, prec);
_acb_vec_clear(t, order);
return 0;
}
void
acb_poly_sin_series(acb_poly_t g, const acb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (hlen == 0 || n == 0)
{
acb_poly_zero(g);
return;
}
if (hlen == 1)
n = 1;
acb_poly_fit_length(g, n);
_acb_poly_sin_series(g->coeffs, h->coeffs, hlen, n, prec);
_acb_poly_set_length(g, n);
_acb_poly_normalise(g);
}