Families of Integrals of Polylogarithmic Functions

Anthony Sofo
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Anthony Sofo: Victoria University, P. O. Box 14428, Melbourne City, Victoria 8001, Australia

Mathematics, 2019, vol. 7, issue 2, 1-20

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.

Keywords: Euler sums; zeta functions; Dirichlet functions; series representation; harmonic number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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