Geodesic
On polylogarithms
Glasgow mathematical journal, Tome 6 (1964) no. 4, pp. 169-171

Voir la notice de l'article provenant de la source Cambridge University Press

The nth order polylogarithm Lin(z) is defined for |z| ≦ 1 by([4, p. 169], cf. [2, §1. 11 (14) and § 1. 11. 1]). The definition can be extended to all values of zin the z-plane cut along the real axis from 1 to ∝ by the formula[2, §1. 11(3)]. Then Lin(z) is regular in the cut plane, and there is a differential recurrence relation [4, p. 169]It is convenient to extend the sequence Lin(z) backwards in the manner suggested by (2) and defineThen Li1(z)= – log(l–z), and Lin(z) is a rational function of z for n= 0, – 1, – 2,.... Formula (2) now holds for all integers n. 
Eastham, M. S. P. On polylogarithms. Glasgow mathematical journal, Tome 6 (1964) no. 4, pp. 169-171. doi: 10.1017/S2040618500034961
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