<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Integrals of polylogarithmic functions with negative argument

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Integrals of polylogarithmic functions with negative argument"}

The connection between polylogarithmic functions and Euler sums is well known. In this paper we explore the representation and many connections between...

Integrals of polylogarithmic functions with negative argument

Published Online: Mar 04, 2019

Page range: 347 - 367

Received: Aug 08, 2018

DOI: https://doi.org/10.2478/ausm-2018-0027

Keywords
polylogarithm function, Euler sums, zeta functions, Dirichlet functions

© 2018 Anthony Sofo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Integrals of polylogarithmic functions with negative argument

Published Online: Mar 04, 2019

Page range: 347 - 367

Received: Aug 08, 2018

DOI: https://doi.org/10.2478/ausm-2018-0027

Keywordspolylogarithm function, Euler sums, zeta functions, Dirichlet functions

© 2018 Anthony Sofo, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
polylogarithm function, Euler sums, zeta functions, Dirichlet functions