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)); }