ABSTRACT
The table of integrals [35] contains many entries that are expressible in terms of the polylogarithm function
(9.1.1) Lis(z) := ∞∑ k=1
zk
ks .
In this paper we describe the evaluation of some of them. The series (9.1.1) converges for |z| < 1 and Re s > 1. The integral representation
(9.1.2) Lis(z) = z
Γ(s)
xs−1 dx ex − z
provides an analytic extension to C. Here Γ(s) is the classical gamma function defined by
(9.1.3) Γ(s) :=
xs−1e−x dx.
