function [ n_data, x, fx ] = trigamma_values ( n_data ) %*****************************************************************************80 % %% TRIGAMMA_VALUES returns some values of the TriGamma function. % % Discussion: % % In Mathematica, the function can be evaluated by: % % PolyGamma[1,x] % % TriGamma(X) = d^2 ln ( Gamma ( X ) ) / d X^2 % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 16 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, real X, the argument of the function. % % Output, real FX, the value of the function. % n_max = 11; fx_vec = [ ... 0.1644934066848226E+01, ... 0.1433299150792759E+01, ... 0.1267377205423779E+01, ... 0.1134253434996619E+01, ... 0.1025356590529597E+01, ... 0.9348022005446793E+00, ... 0.8584318931245799E+00, ... 0.7932328301639984E+00, ... 0.7369741375017002E+00, ... 0.6879720582426356E+00, ... 0.6449340668482264E+00 ]; x_vec = [ ... 1.0E+00, ... 1.1E+00, ... 1.2E+00, ... 1.3E+00, ... 1.4E+00, ... 1.5E+00, ... 1.6E+00, ... 1.7E+00, ... 1.8E+00, ... 1.9E+00, ... 2.0E+00 ]; if ( n_data < 0 ) n_data = 0; end n_data = n_data + 1; if ( n_max < n_data ) n_data = 0; x = 0.0; fx = 0.0; else x = x_vec(n_data); fx = fx_vec(n_data); end return end