#! /usr/bin/env python
#
def lerch ( z, s, a ):

#*****************************************************************************80
#
## LERCH estimates the Lerch transcendent function.
#
#  Discussion:
#
#    The Lerch transcendent function is defined as:
#
#      LERCH ( Z, S, A ) = Sum ( 0 <= K < Infinity ) Z^K / ( A + K )^S
#
#    excluding any term 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:
#
#    23 February 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Eric Weisstein, editor,
#    CRC Concise Encylopedia of Mathematics,
#    CRC Press, 1998.
#
#  Thanks:
#
#    Oscar van Vlijmen
#
#  Parameters:
#
#    Input, real Z, integer S, real A,
#    the parameters of the function.
#
#    Output, real VALUE, an approximation to the Lerch
#    transcendent function.
#
  value = 0.0

  if ( z <= 0.0 ):
    return value

  eps = 1.0E-10
  k = 0
  z_k = 1.0

  while ( True ):

    if ( a + k != 0.0 ):

      term = z_k / ( a + k ) ** s
      value = value + term

      if ( abs ( term ) <= eps * ( 1.0 + abs ( value ) ) ):
        break

    k = k + 1
    z_k = z_k * z

  return value

def lerch_test ( ):

#*****************************************************************************80
#
## LERCH_TEST tests LERCH.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 February 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from lerch_values import lerch_values

  print ( '' )
  print ( 'LERCH_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  LERCH evaluates the Lerch function;' )
  print ( '' )
  print ( '       Z       S       A         Lerch           Lerch' )
  print ( '                             Tabulated        Computed' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, z, s, a, f = lerch_values ( n_data )

    if ( n_data == 0 ):
      break

    f2 = lerch ( z, s, a )

    print ( '  %8g  %4d  %8g  %14g  %14g' % ( z, s, a, f, f2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'LERCH_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  lerch_test ( )
  timestamp ( )