function value = lerch ( a, b, c ) %*****************************************************************************80 % %% LERCH estimates the Lerch transcendent function. % % Discussion: % % The Lerch transcendent function is defined as: % % LERCH ( A, B, C ) = Sum ( 0 <= K < Infinity ) A**K / ( C + K )**B % % excluding any term with ( C + K ) = 0. % % Licensing: % % This code is distributed under the GNU LGPL license. % % Modified: % % 13 September 2004 % % Author: % % John Burkardt % % Reference: % % Eric Weisstein, editor, % CRC Concise Encylopedia of Mathematics, % CRC Press, 1998. % % Thanks: % % Oscar van Vlijmen % % Parameters: % % Input, real A, B, C, the parameters of the function. % % Output, real VALUE, an approximation to the Lerch % transcendent function. % sum2 = 0.0; k = 0; a_k = 1.0; while ( 1 ) sum2_old = sum2; if ( c + k == 0.0 ) k = k + 1; a_k = a_k * a; continue end sum2 = sum2 + a_k / ( c + k )^b; if ( sum2 <= sum2_old ) break end k = k + 1; a_k = a_k * a; end value = sum2; return end