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Mathematics 2019, 7(2), 143; https://doi.org/10.3390/math7020143

Families of Integrals of Polylogarithmic Functions

Victoria University, P. O. Box 14428, Melbourne City, Victoria 8001, Australia
Lovingly dedicated to Mia Eva Manca.
Received: 30 December 2018 / Revised: 23 January 2019 / Accepted: 26 January 2019 / Published: 3 February 2019
(This article belongs to the Special Issue Special Functions and Applications)
Full-Text   |   PDF [271 KB, uploaded 3 February 2019]

Abstract

We give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing new results and further reinforcing the well-known connection between Euler sums and polylogarithmic functions. Many examples of integrals of products of polylogarithmic functions in terms of Riemann zeta values and Dirichlet values will be given. Suggestions for further research are also suggested, including a study of polylogarithmic functions with inverse trigonometric functions. View Full-Text
Keywords: Euler sums; zeta functions; Dirichlet functions; series representation; harmonic number Euler sums; zeta functions; Dirichlet functions; series representation; harmonic number
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Sofo, A. Families of Integrals of Polylogarithmic Functions. Mathematics 2019, 7, 143.

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