# Double Integral Involving Logarithmic and Quotient Function with Powers Expressed in terms of the Lerch Function

## DOI:

https://doi.org/10.29020/nybg.ejpam.v14i4.4085## Keywords:

Catalan's constant, Double integral, Aprey's constant, Lerch function, Contour integral## Abstract

In this work the authors use their contour integral method to derive the double integral given by $\int_{0}^{\infty}\int_{0}^{\infty}\frac{x^{m-1} y^{m+\frac{q}{2}-1} \log ^k(a x y)}{\left(x^q+1\right)^2 \left(y^q+1\right)^2}dxdy$ in terms of the Lerch function. This integral formula is then used to derive closed solutions in terms of fundamental constants and special functions. There are some useful results relating double integrals of certain kinds of functions to ordinary integrals for which we know no general reference. Thus a table of integral pairs is given for interested readers. All the results in this work are new.## Downloads

## Published

2021-11-10

## Issue

## Section

Nonlinear Analysis

## License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to *European Journal of Pure and Applied Mathematics.*

*European Journal of Pure and Applied Mathematics will be Copyright Holder.*

## How to Cite

*European Journal of Pure and Applied Mathematics*,

*14*(4), 1337-1349. https://doi.org/10.29020/nybg.ejpam.v14i4.4085