function [ n_data, n, x, fx ] = legendre_function_q_values ( n_data )

%*****************************************************************************80
%
%% LEGENDRE_FUNCTION_Q_VALUES returns values of the Legendre Q function.
%
%  Discussion:
%
%    In Mathematica, the function can be evaluated by:
%
%      LegendreQ[n,x]
%
%  Differential equation:
%
%    (1-X*X) Y'' - 2 X Y' + N (N+1) = 0
%
%  First terms:
%
%    Q(0)(X) = 0.5 * log((1+X)/(1-X))
%    Q(1)(X) = Q(0)(X)*X - 1 
%    Q(2)(X) = Q(0)(X)*(3*X*X-1)/4 - 1.5*X
%    Q(3)(X) = Q(0)(X)*(5*X*X*X-3*X)/4 - 2.5*X**2 + 2/3
%    Q(4)(X) = Q(0)(X)*(35*X**4-30*X**2+3)/16 - 35/8 * X**3 + 55/24 * X
%    Q(5)(X) = Q(0)(X)*(63*X**5-70*X**3+15*X)/16 - 63/8*X**4 + 49/8*X**2 - 8/15
%
%  Recursion:
%
%    Q(0) = 0.5 * log ( (1+X) / (1-X) )
%    Q(1) = 0.5 * X * log ( (1+X) / (1-X) ) - 1.0
%
%    Q(N) = ( (2*N-1) * X * Q(N-1) - (N-1) * Q(N-2) ) / N
%
%  Restrictions:
%
%    -1 < X < 1
%
%  Special values:
%
%    Note that the Legendre function Q(N)(X) is equal to the
%    associated Legendre function of the second kind,
%    Q(N,M)(X) with M = 0.
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    19 September 2004
%
%  Author:
%
%    John Burkardt
%
%  Reference:
%
%    Milton Abramowitz and Irene Stegun,
%    Handbook of Mathematical Functions,
%    US Department of Commerce, 1964.
%
%    Stephen Wolfram,
%    The Mathematica Book,
%    Fourth Edition,
%    Wolfram Media / Cambridge University Press, 1999.
%
%  Parameters:
%
%    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
%    first call.  On each call, the routine increments N_DATA by 1, and
%    returns the corresponding data; when there is no more data, the
%    output value of N_DATA will be 0 again.
%
%    Output, integer N, the order of the function.
%
%    Output, real X, the point where the function is evaluated.
%
%    Output, real FX, the value of the function.
%
  n_max = 21;

  fx_vec = [ ...
      0.2554128118829953E+00, ...
     -0.9361467970292512E+00, ...
     -0.4787614548274669E+00, ...
      0.4246139251747229E+00, ...
      0.5448396833845414E+00, ...
     -0.9451328261673470E-01, ...
     -0.4973516573531213E+00, ...
     -0.1499018843853194E+00, ...
      0.3649161918783626E+00, ...
      0.3055676545072885E+00, ...
     -0.1832799367995643E+00, ...
      0.6666666666666667E+00, ...
      0.6268672028763330E+00, ...
      0.5099015515315237E+00, ...
      0.3232754180589764E+00, ...
      0.8026113738148187E-01, ...
     -0.1986547714794823E+00, ...
     -0.4828663183349136E+00, ...
     -0.7252886849144386E+00, ...
     -0.8454443502398846E+00, ...
     -0.6627096245052618E+00 ];

  n_vec = [ ...
     0,  1,  2, ...
     3,  4,  5, ...
     6,  7,  8, ...
     9, 10,  3, ...
     3,  3,  3, ...
     3,  3,  3, ...
     3,  3,  3 ];

  x_vec = [ ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.25E+00, ...
     0.00E+00, ...
     0.10E+00, ...
     0.20E+00, ...
     0.30E+00, ...
     0.40E+00, ...
     0.50E+00, ...
     0.60E+00, ...
     0.70E+00, ...
     0.80E+00, ...
     0.90E+00 ];

  if ( n_data < 0 )
    n_data = 0;
  end

  n_data = n_data + 1;

  if ( n_max < n_data )
    n_data = 0;
    n = 0;
    x = 0.0;
    fx = 0.0;
  else
    n = n_vec(n_data);
    x = x_vec(n_data);
    fx = fx_vec(n_data);
  end

  return
end
