Generalizations of Guillera-Sondow's double integral formulas

Abstract

We evaluate certain multidimensional integrals in terms of the Lerch transcendent function $\Phi$, generalizing Guillera-Sondow's formulas. As an application, we get new representations of classical constants like Euler's constant $\gamma$ and $\ln (4/\pi )$.

v2: typos corrected; v3: minor corrections/changes to wording