Some New Transformation Properties of the Nielsen Generalized Polylogarithm

Many of the properties of Nielsen generalized polylogarithm Sn,p(z), for example, the special value and the transformation formulas, play important roles in the computation of higher order radiative corrections in quantum electrodynamics. In this paper, some transformation formulas of z→p(z),p(z)=1-z,1/z,1/(1-z),z/(z-1), and (1-z)/z are obtained. In particular, the last three transformation formulas are new results so far in the literature. By use of these transformation formulas presented, new fast algorithms for Nielsen generalized polylogarithm Sn,p(z) can be designed. For sn,p=Sn,p(1), a new recurrence formula is also given. The identities and the calculation of σn,p and an,p are also investigated