polylog Class Reference

#include <polylog.h>


Detailed Description

Polylogarithms (approximate) $ Li_n(x)$.

This gives an approximation to the polylogarithm functions.

Only works at present for $n=0,1,...,6$. Uses GSL library for n=2.

Uses linear interpolation for $-1<x<0$ and a series expansion for $x<-1$

Todo:
For reference, there are exact relations

\[ \mathrm{Li}_2 \left(\frac{1}{2}\right) = \frac{1}{12}\left[\pi^2-6\left(\ln 2\right)^2\right] \]

\[ \mathrm{Li}_3 \left(\frac{1}{2}\right) = \frac{1}{24}\left[ 4\left(\ln 2\right)^3 - 2 \pi^2 \ln 2 + 21 \zeta (3) \right] \]

\[ \mathrm{Li}_{-1} (x) = \frac{x}{\left(1-x\right)^2} \]

\[ \mathrm{Li}_{-2} (x) = \frac{x\left(x+1\right)}{\left(1-x\right)^3} \]

Definition at line 77 of file polylog.h.


Public Member Functions

double li0 (double x)
 0-th order polylogarithm = $ x/(1-x)$
double li1 (double x)
 1-st order polylogarithm = $ -\ln(1-x) $
double li2 (double x)
 2-nd order polylogarithm
double li3 (double x)
 3-rd order polylogarithm
double li4 (double x)
 4-th order polylogarithm
double li5 (double x)
 5-th order polylogarithm
double li6 (double x)
 6-th order polylogarithm

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