./../src/integrals/three_point/mod_gn.f90

src/integrals/three_point/func_gn [ Modules ]

NAME

  Module func_gn

USAGE

  use func_gn

DESCRIPTION

  This module contains several functions for the computation of
  int^1_0 dx x^(n-1)*ln(a*x^2+b*x+c-i*lambda)/(a*x^2+b*x+c-i*lambda) 
  where a, b and c are real numbers

OUTPUT

  This modules exports three functions:
  * ge -- a function
  * gl -- a function
  * gf -- a function

USES

  * precision_golem (src/module/precision.f90)
  * numerical_evaluation (src/numerical/mod_numeric.f90)
  * sortie_erreur (src/module/sortie_erreur.f90) only : tab_erreur_par,catch_exception,origine_info_par,num_grand_b_info_par,denom_grand_b_info_par
  * parametre (src/module/parametre.f90)
  * logarithme (src/module/z_log.f90)
  * dilogarithme (src/module/zdilog.f90)
  * constante (src/module/constante.f90) only : i_,un,pi

src/integrals/three_point/func_gn/ge [ Functions ]

[ Top ] [ Functions ]

NAME

  Function ge

USAGE

  real_dim2 = ge(n,a,b,c,dist)

DESCRIPTION

  This function computes:
  int^1_0 dx x^(n-1)/(a*x^2+b*x+c-i*lambda) 
  where a, b and c are reals
  It switches to numerical evaluation if 
  (b^2-4*a*c) < coupure_3p1m_2mi
  Around the Landau pole, the divergent part is extracted analytically,
  only the rest is computed numerically

INPUTS

  * n -- an integer, the power of x in the integrand
  * a -- a real (type ki), coefficient of x^2
  * b -- a real (type ki), coefficient of x^1
  * c -- a real (type ki), coefficient of x^0
  * dist -- a logical, true if we are close to the real threshold

SIDE EFFECTS

  No side effect, the returned value depends on the global variables
  rat_or_tot_par, coupure_3p1m_2mi

RETURN VALUE

  It returns a real (type ki) array of rank 1 and shape 2

EXAMPLE

src/integrals/three_point/func_gn/gf [ Functions ]

[ Top ] [ Functions ]

NAME

  Function gf

USAGE

  real_dim2 = gf(n,a,b,c,dist)

DESCRIPTION

  This function computes:
  int^1_0 dx x^(n-1)*ln(a*x^2+b*x+c-i*lambda)/(a*x^2+b*x+c-i*lambda) 
  where a, b and c are reals
  It switches to numerical evaluation if 
  (b^2-4*a*c) < coupure_3p1m_2mi
  Around the Landau pole, the divergent part is extracted analytically,
  only the rest is computed numerically

INPUTS

  * n -- an integer, the power of x in the integrand
  * a -- a real (type ki), coefficient of x^2
  * b -- a real (type ki), coefficient of x^1
  * c -- a real (type ki), coefficient of x^0
  * dist -- a logical, true if we are close to the real threshold

SIDE EFFECTS

  No side effect, the returned value depends on the global variables
  rat_or_tot_par, coupure_3p1m_2mi

RETURN VALUE

  It returns a real (type ki) array of rank 1 and shape 2

EXAMPLE

src/integrals/three_point/func_gn/gl [ Functions ]

[ Top ] [ Functions ]

NAME

  Function gl

USAGE

  real_dim2 = gl(n,a,b,c)

DESCRIPTION

  This function computes:
  int^1_0 dx x^(n-1)*ln(a*x^2+b*x+c-i*lambda) 
  where a, b and c are reals
  here, no need to switch to numerical evaluation
  no numerical problems when (b^2-4*a*c) = 0

INPUTS

  * n -- an integer, the power of x in the integrand
  * a -- a real (type ki), coefficient of x^2
  * b -- a real (type ki), coefficient of x^1
  * c -- a real (type ki), coefficient of x^0

SIDE EFFECTS

  No side effect, the returned value depends on the global variable
  rat_or_tot_par

RETURN VALUE

  It returns a real (type ki) array of rank 1 and shape 2

EXAMPLE