int
gsl_sf_bessel_Ynu_e(double nu, double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(x <= 0.0 || nu < 0.0) {
DOMAIN_ERROR(result);
}
else if(nu > 50.0) {
return gsl_sf_bessel_Ynu_asymp_Olver_e(nu, x, result);
}
else {
/* -1/2 <= mu <= 1/2 */
int N = (int)(nu + 0.5);
double mu = nu - N;
gsl_sf_result Y_mu, Y_mup1;
int stat_mu;
double Ynm1;
double Yn;
double Ynp1;
int n;
if(x < 2.0) {
/* Determine Ymu, Ymup1 directly. This is really
* an optimization since this case could as well
* be handled by a call to gsl_sf_bessel_JY_mu_restricted(),
* as below.
*/
stat_mu = gsl_sf_bessel_Y_temme(mu, x, &Y_mu, &Y_mup1);
}
else {
/* Determine Ymu, Ymup1 and Jmu, Jmup1.
*/
gsl_sf_result J_mu, J_mup1;
stat_mu = gsl_sf_bessel_JY_mu_restricted(mu, x, &J_mu, &J_mup1, &Y_mu, &Y_mup1);
}
/* Forward recursion to get Ynu, Ynup1.
*/
Ynm1 = Y_mu.val;
Yn = Y_mup1.val;
for(n=1; n<=N; n++) {
Ynp1 = 2.0*(mu+n)/x * Yn - Ynm1;
Ynm1 = Yn;
Yn = Ynp1;
}
result->val = Ynm1; /* Y_nu */
result->err = (N + 1.0) * fabs(Ynm1) * (fabs(Y_mu.err/Y_mu.val) + fabs(Y_mup1.err/Y_mup1.val));
result->err += 2.0 * GSL_DBL_EPSILON * fabs(Ynm1);
return stat_mu;
}
}
int gsl_sf_bessel_yl_e(int l, const double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(l < 0 || x <= 0.0) {
DOMAIN_ERROR(result);
}
else if(l == 0) {
return gsl_sf_bessel_y0_e(x, result);
}
else if(l == 1) {
return gsl_sf_bessel_y1_e(x, result);
}
else if(l == 2) {
return gsl_sf_bessel_y2_e(x, result);
}
else if(x < 3.0) {
return bessel_yl_small_x(l, x, result);
}
else if(GSL_ROOT3_DBL_EPSILON * x > (l*l + l + 1.0)) {
int status = gsl_sf_bessel_Ynu_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(l > 40) {
int status = gsl_sf_bessel_Ynu_asymp_Olver_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_by;
gsl_sf_result r_bym;
int stat_1 = gsl_sf_bessel_y1_e(x, &r_by);
int stat_0 = gsl_sf_bessel_y0_e(x, &r_bym);
double bym = r_bym.val;
double by = r_by.val;
double byp;
int j;
for(j=1; j<l; j++) {
byp = (2*j+1)/x*by - bym;
bym = by;
by = byp;
}
result->val = by;
result->err = fabs(result->val) * (GSL_DBL_EPSILON + fabs(r_by.err/r_by.val) + fabs(r_bym.err/r_bym.val));
return GSL_ERROR_SELECT_2(stat_1, stat_0);
}
}
int
gsl_sf_bessel_Yn_e(int n, const double x, gsl_sf_result * result)
{
int sign = 1;
if(n < 0) {
/* reduce to case n >= 0 */
n = -n;
if(GSL_IS_ODD(n)) sign = -1;
}
/* CHECK_POINTER(result) */
if(n == 0) {
int status = gsl_sf_bessel_Y0_e(x, result);
result->val *= sign;
return status;
}
else if(n == 1) {
int status = gsl_sf_bessel_Y1_e(x, result);
result->val *= sign;
return status;
}
else {
if(x <= 0.0) {
DOMAIN_ERROR(result);
}
if(x < 5.0) {
int status = bessel_Yn_small_x(n, x, result);
result->val *= sign;
return status;
}
else if(GSL_ROOT3_DBL_EPSILON * x > (n*n + 1.0)) {
int status = gsl_sf_bessel_Ynu_asympx_e((double)n, x, result);
result->val *= sign;
return status;
}
else if(n > 50) {
int status = gsl_sf_bessel_Ynu_asymp_Olver_e((double)n, x, result);
result->val *= sign;
return status;
}
else {
double two_over_x = 2.0/x;
gsl_sf_result r_by;
gsl_sf_result r_bym;
int stat_1 = gsl_sf_bessel_Y1_e(x, &r_by);
int stat_0 = gsl_sf_bessel_Y0_e(x, &r_bym);
double bym = r_bym.val;
double by = r_by.val;
double byp;
int j;
for(j=1; j<n; j++) {
byp = j*two_over_x*by - bym;
bym = by;
by = byp;
}
result->val = sign * by;
result->err = fabs(result->val) * (fabs(r_by.err/r_by.val) + fabs(r_bym.err/r_bym.val));
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
return GSL_ERROR_SELECT_2(stat_1, stat_0);
}
}
}
