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transcendental_fct_type_B Class Reference

#include <transc_fct_B.h>

List of all members.

Public Member Functions

 transcendental_fct_type_B (const GiNaC::ex &xx1, const GiNaC::ex &xx2, const GiNaC::ex &ii_num, const GiNaC::ex &ii_denom, const GiNaC::ex &jj_num, const GiNaC::ex &jj_denom, const GiNaC::ex &iijj_num, const GiNaC::ex &iijj_denom, const GiNaC::ex &pp_num, const GiNaC::ex &pp_denom)
 transcendental_fct_type_B (const GiNaC::ex &xx1, const GiNaC::ex &xx2, const GiNaC::ex &ii_num, const GiNaC::ex &ii_denom, const GiNaC::ex &jj_num, const GiNaC::ex &jj_denom, const GiNaC::ex &iijj_num, const GiNaC::ex &iijj_denom, const GiNaC::ex &pp_num, const GiNaC::ex &pp_denom, const GiNaC::ex &eps, int o, int f)
void archive (GiNaC::archive_node &node) const
void read_archive (const GiNaC::archive_node &node, GiNaC::lst &sym_lst)
unsigned return_type (void) const
void print (const GiNaC::print_context &c, unsigned level=0) const
unsigned precedence (void) const
GiNaC::ex eval (int level=0) const
GiNaC::ex subs (const GiNaC::exmap &m, unsigned options=0) const
GiNaC::ex set_expansion (const GiNaC::ex &eps, int o) const
GiNaC::ex shift_plus_one (void) const

Protected Member Functions

GiNaC::ex eval_ncmul (const GiNaC::exvector &v) const
GiNaC::ex derivative (const GiNaC::symbol &s) const
unsigned calchash (void) const

Protected Attributes

GiNaC::ex x1
GiNaC::ex x2
GiNaC::ex i_num
GiNaC::ex i_denom
GiNaC::ex j_num
GiNaC::ex j_denom
GiNaC::ex ij_num
GiNaC::ex ij_denom
GiNaC::ex pre_num
GiNaC::ex pre_denom
GiNaC::ex expansion_parameter
int order
int flag_expand_status

Detailed Description

The definition is

\[ \frac{\Gamma(d_1) ... \Gamma(d_n)}{\Gamma(d_1') ... \Gamma(d_{n'}')} \sum\limits_{i=0}^\infty \sum\limits_{j=0}^\infty \frac{\Gamma(i+a_1) ... \Gamma(i+a_k)}{\Gamma(i+a_1') ... \Gamma(i+a_{k-1}')} \frac{\Gamma(j+b_1) ... \Gamma(j+b_l)}{\Gamma(j+b_1') ... \Gamma(j+b_{l-1}')} \frac{\Gamma(i+j+c_1) ... \Gamma(i+j+c_m)}{\Gamma(i+j+c_1') ... \Gamma(i+j+c_{m}')} \frac{x_1^i}{i!} \frac{x_2^j}{j!} \]

Member Function Documentation

ex eval (  int  level = 0  )  const
 

Evaluation: If flag_expand_status is set, the object is expanded in $\varepsilon$.

The result is converted to a standard form, using convert_Zsums_to_standard_form.

ex eval_ncmul (  const GiNaC::exvector &  v  )  const [protected]
 

No automatic simplifications

ex set_expansion (  const GiNaC::ex &  eps,
int  o
)  const
 

Sets the flag flag_expand_status to expand_status::expansion_required. The object is then automatically expanded up to the specified order.

ex shift_plus_one (  void   )  const
 

Casts a sum of the form

\[ \frac{\Gamma(d_1) ... \Gamma(d_n)}{\Gamma(d_1') ... \Gamma(d_{n'}')} \sum\limits_{i=1}^\infty \sum\limits_{j=1}^\infty \frac{\Gamma(i+a_1) ... \Gamma(i+a_k)}{\Gamma(i+a_1') ... \Gamma(i+a_{k-1}')} \frac{\Gamma(j+b_1) ... \Gamma(j+b_l)}{\Gamma(j+b_1') ... \Gamma(j+b_{l-1}')} \frac{\Gamma(i+j+c_1) ... \Gamma(i+j+c_m)}{\Gamma(i+j+c_1') ... \Gamma(i+j+c_{m}')} \frac{x_1^i}{i!} \frac{x_2^j}{j!} \]

into the form of transcendental_fct_type_B by making the change of variables

\[ i' = i-1 \]

\[ j' = j-1 \]

The documentation for this class was generated from the following files:
Generated on Wed Jun 10 22:59:11 2009 for Nestedsums library by doxygen 1.3.7