Explicit Formulas For Generalized Polylogarithmic Integrals, Euler Sums, And BBP-Type Series

Abstract: This paper explores closed-form expressions for some polylogarithm integrals with integrands containing five parameters. These closed form expressions are given in terms of the Lerch transcendent function, which reduces, in some cases, to well-known special functions, such as the Riemann zeta, Dirichlet eta, Dirichlet beta, the Hurwitz zeta, and the polygamma functions. Related Euler sums and BBP-type series will also be discussed.