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);
}
}
int gsl_sf_bessel_Kn_scaled_e(int n, const double x, gsl_sf_result * result)
{
n = abs(n); /* K(-n, z) = K(n, z) */
/* CHECK_POINTER(result) */
if(x <= 0.0) {
DOMAIN_ERROR(result);
}
else if(n == 0) {
return gsl_sf_bessel_K0_scaled_e(x, result);
}
else if(n == 1) {
return gsl_sf_bessel_K1_scaled_e(x, result);
}
else if(x <= 5.0) {
return bessel_Kn_scaled_small_x(n, x, result);
}
else if(GSL_ROOT3_DBL_EPSILON * x > 0.25 * (n*n + 1)) {
return gsl_sf_bessel_Knu_scaled_asympx_e((double)n, x, result);
}
else if(GSL_MIN(0.29/(n*n), 0.5/(n*n + x*x)) < GSL_ROOT3_DBL_EPSILON) {
return gsl_sf_bessel_Knu_scaled_asymp_unif_e((double)n, x, result);
}
else {
/* Upward recurrence. [Gradshteyn + Ryzhik, 8.471.1] */
double two_over_x = 2.0/x;
gsl_sf_result r_b_jm1;
gsl_sf_result r_b_j;
int stat_0 = gsl_sf_bessel_K0_scaled_e(x, &r_b_jm1);
int stat_1 = gsl_sf_bessel_K1_scaled_e(x, &r_b_j);
double b_jm1 = r_b_jm1.val;
double b_j = r_b_j.val;
double b_jp1;
int j;
for(j=1; j<n; j++) {
b_jp1 = b_jm1 + j * two_over_x * b_j;
b_jm1 = b_j;
b_j = b_jp1;
}
result->val = b_j;
result->err = n * (fabs(b_j) * (fabs(r_b_jm1.err/r_b_jm1.val) + fabs(r_b_j.err/r_b_j.val)));
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_2(stat_0, stat_1);
}
}
