Integrals of polylogarithmic functions with negative argument

Anthony Sofo

doi:10.2478/ausm-2018-0027

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Integrals of polylogarithmic functions with negative argument

Acta Universitatis Sapientiae, Mathematica

Volume 10 (2018): Issue 2 (December 2018)

By: Anthony Sofo

Open Access

|Mar 2019

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/ausm-2018-0027 | Journal eISSN: 2066-7752

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Language: English

Page range: 347 - 367

Submitted on: Aug 8, 2018

Published online: Mar 4, 2019

Published in print: Dec 1, 2018

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Keywords:

polylogarithm function,

Euler sums,

zeta functions,

Dirichlet functions

MSC:

11M06,

11M32,

33B15

Related subjects:

Mathematics,

General mathematics

© 2019 Anthony Sofo, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 10 (2018): Issue 2 (December 2018)