function [ n_data, z, s, a, fx ] = lerch_values ( n_data ) %*****************************************************************************80 % %% LERCH_VALUES returns some values of the Lerch transcendent function. % % Discussion: % % The Lerch function is defined as % % Phi(z,s,a) = Sum ( 0 <= k < Infinity ) z^k / ( a + k )^s % % omitting any terms with ( a + k ) = 0. % % In Mathematica, the function can be evaluated by: % % LerchPhi[z,s,a] % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 19 September 2004 % % Author: % % John Burkardt % % Reference: % % 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 Z, the parameters of the function. % % Output, integer S, the parameters of the function. % % Output, real A, the parameters of the function. % % Output, real FX, the value of the function. % n_max = 12; a_vec = [ ... 0.0, ... 0.0, ... 0.0, ... 1.0, ... 1.0, ... 1.0, ... 2.0, ... 2.0, ... 2.0, ... 3.0, ... 3.0, ... 3.0 ]; fx_vec = [ ... 0.1644934066848226E+01, ... 0.1202056903159594E+01, ... 0.1000994575127818E+01, ... 0.1164481052930025E+01, ... 0.1074426387216080E+01, ... 0.1000492641212014E+01, ... 0.2959190697935714E+00, ... 0.1394507503935608E+00, ... 0.9823175058446061E-03, ... 0.1177910993911311E+00, ... 0.3868447922298962E-01, ... 0.1703149614186634E-04 ]; s_vec = [ ... 2, 3, 10, ... 2, 3, 10, ... 2, 3, 10, ... 2, 3, 10 ]; z_vec = [ ... 0.1000000000000000E+01, ... 0.1000000000000000E+01, ... 0.1000000000000000E+01, ... 0.5000000000000000E+00, ... 0.5000000000000000E+00, ... 0.5000000000000000E+00, ... 0.3333333333333333E+00, ... 0.3333333333333333E+00, ... 0.3333333333333333E+00, ... 0.1000000000000000E+00, ... 0.1000000000000000E+00, ... 0.1000000000000000E+00 ]; if ( n_data < 0 ) n_data = 0; end n_data = n_data + 1; if ( n_max < n_data ) n_data = 0; z = 0.0; s = 0; a = 0.0; fx = 0.0; else z = z_vec(n_data); s = s_vec(n_data); a = a_vec(n_data); fx = fx_vec(n_data); end return end