/* [Abramowitz+Stegun, 9.6.11]
* assumes n >= 1
*/
static
int
bessel_Kn_scaled_small_x(const int n, const double x, gsl_sf_result * result)
{
int k;
double y = 0.25 * x * x;
double ln_x_2 = log(0.5*x);
double ex = exp(x);
gsl_sf_result ln_nm1_fact;
double k_term;
double term1, sum1, ln_pre1;
double term2, sum2, pre2;
gsl_sf_lnfact_e((unsigned int)(n-1), &ln_nm1_fact);
ln_pre1 = -n*ln_x_2 + ln_nm1_fact.val;
if(ln_pre1 > GSL_LOG_DBL_MAX - 3.0) GSL_ERROR ("error", GSL_EOVRFLW);
sum1 = 1.0;
k_term = 1.0;
for(k=1; k<=n-1; k++) {
k_term *= -y/(k * (n-k));
sum1 += k_term;
}
term1 = 0.5 * exp(ln_pre1) * sum1;
pre2 = 0.5 * exp(n*ln_x_2);
if(pre2 > 0.0) {
const int KMAX = 20;
gsl_sf_result psi_n;
gsl_sf_result npk_fact;
double yk = 1.0;
double k_fact = 1.0;
double psi_kp1 = -M_EULER;
double psi_npkp1;
gsl_sf_psi_int_e(n, &psi_n);
gsl_sf_fact_e((unsigned int)n, &npk_fact);
psi_npkp1 = psi_n.val + 1.0/n;
sum2 = (psi_kp1 + psi_npkp1 - 2.0*ln_x_2)/npk_fact.val;
for(k=1; k<KMAX; k++) {
psi_kp1 += 1.0/k;
psi_npkp1 += 1.0/(n+k);
k_fact *= k;
npk_fact.val *= n+k;
yk *= y;
k_term = yk*(psi_kp1 + psi_npkp1 - 2.0*ln_x_2)/(k_fact*npk_fact.val);
sum2 += k_term;
}
term2 = ( GSL_IS_ODD(n) ? -1.0 : 1.0 ) * pre2 * sum2;
}
else {
term2 = 0.0;
}
result->val = ex * (term1 + term2);
result->err = ex * GSL_DBL_EPSILON * (fabs(ln_pre1)*fabs(term1) + fabs(term2));
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_SUCCESS;
}
double gsl_sf_psi_int(const int n)
{
EVAL_RESULT(gsl_sf_psi_int_e(n, &result));
}
