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); } }