Integrals of polylogarithmic functions with negative argument

Abstract

The connection between polylogarithmic functions and Euler sums is well known. In this paper we explore the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider mainly, polylogarithmic functions with negative arguments, thereby producing new results and extending the work of Freitas. Many examples of integrals of products of polylogarithmic functions in terms of Riemann zeta values and Dirichlet values will be given.

Keywords

• polylogarithm function
• euler sums
• zeta functions
• dirichlet functions
• 11m06
• 11m32
• 33b15