int gsl_sf_bessel_il_scaled_array(const int lmax, const double x, double * result_array)
{
if(x == 0.0) {
int ell;
result_array[0] = 1.0;
for (ell = lmax; ell >= 1; ell--) {
result_array[ell] = 0.0;
};
return GSL_SUCCESS;
} else {
int ell;
gsl_sf_result r_iellp1;
gsl_sf_result r_iell;
int stat_0 = gsl_sf_bessel_il_scaled_e(lmax+1, x, &r_iellp1);
int stat_1 = gsl_sf_bessel_il_scaled_e(lmax, x, &r_iell);
double iellp1 = r_iellp1.val;
double iell = r_iell.val;
double iellm1;
result_array[lmax] = iell;
for(ell = lmax; ell >= 1; ell--) {
iellm1 = iellp1 + (2*ell + 1)/x * iell;
iellp1 = iell;
iell = iellm1;
result_array[ell-1] = iellm1;
}
return GSL_ERROR_SELECT_2(stat_0, stat_1);
}
}
/// Regular modified spherical bessel functions.
double
bessel_il(unsigned int n, double x)
{
gsl_sf_result result;
int stat = gsl_sf_bessel_il_scaled_e(n, x, &result);
if (stat != GSL_SUCCESS)
{
std::ostringstream msg("Error in bessel_il:");
msg << " n=" << n << " x=" << x;
throw std::runtime_error(msg.str());
}
else
return std::exp(std::abs(x)) * result.val;
}
double hyper_helper_function(double rho, void * params) {
hyper_integrand_helper *helper = (hyper_integrand_helper *) params;
double u = (*helper->transformed_state)[0];
double v = (*helper->transformed_state)[2];
double w = (*helper->transformed_state)[1];
double h = helper->h;
double rsqr = h * h - (helper->eta) * rho * rho;
//cout << h << " " << rsqr << " " << rho << endl;
if (rsqr < 0) {
//cout << h << " " << helper->eta << " " << rho << endl;
return 0.0; // in this case there is no point that satisfies the delta function
}
//double r = sqrt(abs(rsqr));
double r = sqrt(rsqr);
//cout << rsqr << endl;
double arg = rho * r * abs(w);
double temp1 = -0.5 * (u * r * r + v * rho * rho);
double temp2 = pow(r, 2*helper->nr + helper->kappa + 1) * pow(rho, 2*helper->nrho + helper->kappa + 2) * h;
double res = 0.0;
//cout << temp1 << " " << temp2 << " " << arg << endl;
if (abs(w/u) < 1E-8) {
if (helper->kappa != 0) {
return 0.0;
}
res = exp(temp1) * temp2 / sqrt(Pi / 2.0);
}
else {
gsl_sf_result bes1;
int status = gsl_sf_bessel_il_scaled_e(helper->kappa, arg, &bes1);
if (status != 0) {
bes1.val = 1.0 / arg;
}
res = bes1.val * exp(abs(arg) + temp1) * temp2 * epsilon(helper->kappa, w) * sqrt(2.0 * helper->kappa + 1.0) / sqrt(Pi / 2.0);
}
//cout << res << " " ;
return res;
}
/* [Abramowitz+Stegun, 10.2.4 + 10.2.6]
* with lmax=15, precision ~ 15D for x < 3
*
* assumes l >= 1
*/
static int bessel_kl_scaled_small_x(int l, const double x, gsl_sf_result * result)
{
gsl_sf_result num_fact;
double den = gsl_sf_pow_int(x, l+1);
int stat_df = gsl_sf_doublefact_e((unsigned int) (2*l-1), &num_fact);
if(stat_df != GSL_SUCCESS || den == 0.0) {
OVERFLOW_ERROR(result);
}
else {
const int lmax = 50;
gsl_sf_result ipos_term;
double ineg_term;
double sgn = (GSL_IS_ODD(l) ? -1.0 : 1.0);
double ex = exp(x);
double t = 0.5*x*x;
double sum = 1.0;
double t_coeff = 1.0;
double t_power = 1.0;
double delta;
int stat_il;
int i;
for(i=1; i<lmax; i++) {
t_coeff /= i*(2*(i-l) - 1);
t_power *= t;
delta = t_power*t_coeff;
sum += delta;
if(fabs(delta/sum) < GSL_DBL_EPSILON) break;
}
stat_il = gsl_sf_bessel_il_scaled_e(l, x, &ipos_term);
ineg_term = sgn * num_fact.val/den * sum;
result->val = -sgn * 0.5*M_PI * (ex*ipos_term.val - ineg_term);
result->val *= ex;
result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return stat_il;
}
}
double gsl_sf_bessel_il_scaled(const int l, const double x)
{
EVAL_RESULT(gsl_sf_bessel_il_scaled_e(l, x, &result));
}
