/* [Abramowitz+Stegun, 10.1.3]
* with lmax=15, precision ~ 15D for x < 3
*
* checked OK [GJ] Wed May 13 15:41:25 MDT 1998
*/
static int bessel_yl_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(2*l-1, &num_fact);
if(stat_df != GSL_SUCCESS || den == 0.0) {
OVERFLOW_ERROR(result);
}
else {
const int lmax = 200;
double t = -0.5*x*x;
double sum = 1.0;
double t_coeff = 1.0;
double t_power = 1.0;
double delta;
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) < 0.5*GSL_DBL_EPSILON) break;
}
result->val = -num_fact.val/den * sum;
result->err = GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
}
/// Double factorial.
double
double_factorial(int n)
{
gsl_sf_result result;
int stat = gsl_sf_doublefact_e(n, &result);
if (stat != GSL_SUCCESS)
{
std::ostringstream msg("Error in double_factorial:");
msg << " n=" << n;
throw std::runtime_error(msg.str());
}
else
return result.val;
}
/* [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;
}
}
