Affiliation:
1. Victoria University, P. O. Box 14428, Melbourne City, Victoria 8001, Australia
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 with alternating signs in the argument and Euler sums. We shall consider mainly, polylogarithmic functions with negative and positive 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.
Publisher
World Scientific Pub Co Pte Lt
Cited by
4 articles.
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1. Parameterized Families of PolyLog Integrals;Constructive Mathematical Analysis;2021-12-02
2. Explicit evaluation of some integrals involving polylogarithm functions;Integral Transforms and Special Functions;2021-06-06
3. Integrals involving the Legendre Chi function;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2020-11-20
4. General order Euler sums with rational argument;Integral Transforms and Special Functions;2019-07-22