Double Integral of Logarithm and Exponential Function Expressed in terms of the Lerch Function

Robert Reynolds, Allan Stauffer

Abstract

This paper contains new explicit computations of some integrals containing elementary functions, such as powers, logarithms, exponentials. In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind $K_{\nu}(z)$ and express it in terms of the Lerch function. A table of integral pairs is given for interested readers. The majority of the results in this work are new.

Keywords

Double integral; Lerch function; Contour integral; Glaisher's constant; modified Bessel function of the second kind

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