int
gsl_sf_hydrogenicR_e(const int n, const int l,
const double Z, const double r,
gsl_sf_result * result)
{
if(n < 1 || l > n-1 || Z <= 0.0 || r < 0.0) {
DOMAIN_ERROR(result);
}
else {
double A = 2.0*Z/n;
gsl_sf_result norm;
int stat_norm = R_norm(n, l, Z, &norm);
double rho = A*r;
double ea = exp(-0.5*rho);
double pp = gsl_sf_pow_int(rho, l);
gsl_sf_result lag;
int stat_lag = gsl_sf_laguerre_n_e(n-l-1, 2*l+1, rho, &lag);
double W_val = norm.val * ea * pp;
double W_err = norm.err * ea * pp;
W_err += norm.val * ((0.5*rho + 1.0) * GSL_DBL_EPSILON) * ea * pp;
W_err += norm.val * ea * ((l+1.0) * GSL_DBL_EPSILON) * pp;
result->val = W_val * lag.val;
result->err = W_val * lag.err + W_err * fabs(lag.val);
result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);
if ((l == 0 || (r > 0 && l > 0)) && lag.val != 0.0
&& stat_lag == GSL_SUCCESS && stat_norm == GSL_SUCCESS) {
CHECK_UNDERFLOW(result);
};
return GSL_ERROR_SELECT_2(stat_lag, stat_norm);
}
}
static VALUE rb_gsl_sf_laguerre_n_e(VALUE obj, VALUE n, VALUE a, VALUE x)
{
gsl_sf_result *rslt = NULL;
VALUE v;
// local variable "status" declared and set, but never used
//int status;
CHECK_FIXNUM(n);
Need_Float(a); Need_Float(x);
v = Data_Make_Struct(cgsl_sf_result, gsl_sf_result, 0, free, rslt);
/*status =*/ gsl_sf_laguerre_n_e(FIX2INT(n), NUM2DBL(a), NUM2DBL(x), rslt);
return v;
}
/// Associated Laguerre polynomials.
double
assoc_laguerre(unsigned int n, unsigned int m, double x)
{
gsl_sf_result result;
int stat = gsl_sf_laguerre_n_e(static_cast<int>(n), static_cast<int>(m), x, &result);
if (stat != GSL_SUCCESS)
{
std::ostringstream msg("Error in assoc_laguerre:");
msg << " n=" << n << " m=" << m << " x=" << x;
throw std::runtime_error(msg.str());
}
else
return result.val;
}
