int
gsl_sf_bessel_kl_scaled_array(const int lmax, const double x, double * result_array)
{
if(lmax < 0 || x <= 0.0) {
GSL_ERROR("domain error", GSL_EDOM);
} else if (lmax == 0) {
gsl_sf_result result;
int stat = gsl_sf_bessel_k0_scaled_e(x, &result);
result_array[0] = result.val;
return stat;
} else {
int ell;
double kellp1, kell, kellm1;
gsl_sf_result r_kell;
gsl_sf_result r_kellm1;
gsl_sf_bessel_k1_scaled_e(x, &r_kell);
gsl_sf_bessel_k0_scaled_e(x, &r_kellm1);
kell = r_kell.val;
kellm1 = r_kellm1.val;
result_array[0] = kellm1;
result_array[1] = kell;
for(ell = 1; ell < lmax; ell++) {
kellp1 = (2*ell+1)/x * kell + kellm1;
result_array[ell+1] = kellp1;
kellm1 = kell;
kell = kellp1;
}
return GSL_SUCCESS;
}
}
int gsl_sf_bessel_kl_scaled_e(int l, const double x, gsl_sf_result * result)
{
if(l < 0 || x <= 0.0) {
DOMAIN_ERROR(result);
}
else if(l == 0) {
return gsl_sf_bessel_k0_scaled_e(x, result);
}
else if(l == 1) {
return gsl_sf_bessel_k1_scaled_e(x, result);
}
else if(l == 2) {
return gsl_sf_bessel_k2_scaled_e(x, result);
}
else if(x < 3.0) {
return bessel_kl_scaled_small_x(l, x, result);
}
else if(GSL_ROOT3_DBL_EPSILON * x > (l*l + l + 1)) {
int status = gsl_sf_bessel_Knu_scaled_asympx_e(l + 0.5, x, result);
double pre = sqrt((0.5*M_PI)/x);
result->val *= pre;
result->err *= pre;
return status;
}
else if(GSL_MIN(0.29/(l*l+1.0), 0.5/(l*l+1.0+x*x)) < GSL_ROOT3_DBL_EPSILON) {
int status = gsl_sf_bessel_Knu_scaled_asymp_unif_e(l + 0.5, x, result);
double pre = sqrt((0.5*M_PI)/x);
result->val *= pre;
result->err *= pre;
return status;
}
else {
/* recurse upward */
gsl_sf_result r_bk;
gsl_sf_result r_bkm;
int stat_1 = gsl_sf_bessel_k1_scaled_e(x, &r_bk);
int stat_0 = gsl_sf_bessel_k0_scaled_e(x, &r_bkm);
double bkp;
double bk = r_bk.val;
double bkm = r_bkm.val;
int j;
for(j=1; j<l; j++) {
bkp = (2*j+1)/x*bk + bkm;
bkm = bk;
bk = bkp;
}
result->val = bk;
result->err = fabs(bk) * (fabs(r_bk.err/r_bk.val) + fabs(r_bkm.err/r_bkm.val));
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_2(stat_1, stat_0);
}
}
double gsl_sf_bessel_k0_scaled(const double x)
{
EVAL_RESULT(gsl_sf_bessel_k0_scaled_e(x, &result));
}
