ClausenFunctions Class Reference

A class for the Clausen functions. More...

#include <ClausenFunctions.h>

Inheritance diagram for ClausenFunctions:

Detailed Description

A class for the Clausen functions.

Author

HEPfit Collaboration

Copyright

GNU General Public License

This class handles the Clausen functions \(\mathrm{Cl}_2(\phi)\) and \(\mathrm{Cl}_3(\phi)\).

Definition at line 22 of file ClausenFunctions.h.

Public Member Functions
double	Cl2 (const double phi) const
	The Clausen function of index 2, \(\mathrm{Cl}_2(\phi)\). More...
double	Cl3 (const double phi) const
	The Clausen function of index 3, \(\mathrm{Cl}_3(\phi)\). More...
	ClausenFunctions ()
	The default constructor. More...
Public Member Functions inherited from BernoulliNumbers
	BernoulliNumbers ()
	The default constructor. More...

Additional Inherited Members
Protected Attributes inherited from BernoulliNumbers
double	B [19]
	the Bernoulli numbers More...

Constructor & Destructor Documentation

ClausenFunctions()

ClausenFunctions::ClausenFunctions

(

)

The default constructor.

Definition at line 15 of file ClausenFunctions.cpp.

{
}

Member Function Documentation

Cl2()

double ClausenFunctions::Cl2

(

const double

phi

)

const

The Clausen function of index 2, \(\mathrm{Cl}_2(\phi)\).

This function calls the GSL function gsl_sf_clausen().

Parameters

[in]

phi

a real variable

Returns

\(\mathrm{Cl}_2(\phi)\)

Definition at line 21 of file ClausenFunctions.cpp.

{
    return ( gsl_sf_clausen(phi) );    
}

Cl3()

double ClausenFunctions::Cl3

(

const double

phi

)

const

The Clausen function of index 3, \(\mathrm{Cl}_3(\phi)\).

The function \(\mathrm{Cl}_3(\phi)\) is computed with the help of the GSL function gsl_sf_zeta_int(3). See [Kniehl:1989qu].

Parameters

[in]

phi

a real variable

Returns

\(\mathrm{Cl}_3(\phi) = \zeta(3) - \phi^2 \left( \frac{3}{4} - \frac{\ln(\phi)}{2} + \sum_{n=1}^{\infty} \frac{B_n \phi^{2n}}{2n(2n+1)(2n+2)(2n)!} \right)\)

Note

The function is even, so the argument is internally reduced to the range [0, pi]. The sum is truncated at n=18.

The Bernoulli numbers are stored in the base class BernoulliNumbers.

Definition at line 26 of file ClausenFunctions.cpp.

{
    auto myphi = remainder(phi, 2.0 * M_PI);   // reduce phi to the range [-pi, pi]
    if (myphi < 0.0) myphi = -myphi; // Clausen function of third order is even, so we can use the positive value
 
    if (myphi==0.0) return ( gsl_sf_zeta_int(3) );
 
    double TMP = 0.0, l_double = 0.0, lfactorial = 1.0, sign = 1.0;
    for (int l=2; l<19; l++) {
        l_double = (double)l;
        lfactorial *= l_double;
        if (l%4) { sign = - 1.0; } else { sign = 1.0; }
        TMP += B[l]*pow(myphi,l_double)/l_double/(l_double + 1.0)/(l_double + 2.0)
               /lfactorial * sign;
    }
    return ( gsl_sf_zeta_int(3) - myphi*myphi*(3.0/4.0 - log(myphi)/2.0 - TMP) );
}

---

The documentation for this class was generated from the following files:

• ClausenFunctions.h
• ClausenFunctions.cpp