Families of integrals of polylogarithmic functions

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Sofo, Anthony ORCID: 0000-0002-1277-8296 (2019) Families of integrals of polylogarithmic functions. Mathematics, 7 (2). ISSN 2227-7390

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.

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Item type Article
URI https://vuir.vu.edu.au/id/eprint/45961
DOI 10.3390/math7020143
Official URL https://www.mdpi.com/2227-7390/7/2/143
Subjects Current > FOR (2020) Classification > 4901 Applied mathematics
Current > Division/Research > College of Science and Engineering
Keywords applied mathematics, polylogarithmic functions, integrals, Eurler sums
Citations in Scopus 4 - View on Scopus
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