function [ n_data, n, x, fx ] = bernoulli_poly_values ( n_data ) %*****************************************************************************80 % %% BERNOULLI_POLY_VALUES returns some values of the Bernoulli polynomials. % % Discussion: % % In Mathematica, the function can be evaluated by: % % BernoulliB[n,x] % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 15 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 Bernoulli polynomial. % % Output, real X, the argument of the Bernoulli polynomial. % % Output, real FX, the value of the Bernoulli polynomial. % n_max = 27; fx_vec = [ ... 0.1000000000000000E+01, ... -0.3000000000000000E+00, ... 0.6666666666666667E-02, ... 0.4800000000000000E-01, ... -0.7733333333333333E-02, ... -0.2368000000000000E-01, ... 0.6913523809523810E-02, ... 0.2490880000000000E-01, ... -0.1014997333333333E-01, ... -0.4527820800000000E-01, ... 0.2332631815757576E-01, ... -0.3125000000000000E+00, ... -0.1142400000000000E+00, ... -0.0176800000000000E+00, ... 0.0156800000000000E+00, ... 0.0147400000000000E+00, ... 0.0000000000000000E+00, ... -0.1524000000000000E-01, ... -0.2368000000000000E-01, ... -0.2282000000000000E-01, ... -0.1376000000000000E-01, ... 0.0000000000000000E+01, ... 0.1376000000000000E-01, ... 0.2282000000000000E-01, ... 0.2368000000000000E-01, ... 0.1524000000000000E-01, ... 0.0000000000000000E+01 ]; n_vec = [ ... 0, ... 1, ... 2, ... 3, ... 4, ... 5, ... 6, ... 7, ... 8, ... 9, ... 10, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5, ... 5 ]; x_vec = [ ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... 0.2E+00, ... -0.5E+00, ... -0.4E+00, ... -0.3E+00, ... -0.2E+00, ... -0.1E+00, ... 0.0E+00, ... 0.1E+00, ... 0.2E+00, ... 0.3E+00, ... 0.4E+00, ... 0.5E+00, ... 0.6E+00, ... 0.7E+00, ... 0.8E+00, ... 0.9E+00, ... 1.0E+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