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

Authors

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.

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How to Cite

Reynolds, R., & Stauffer, A. (2021). Double Integral Involving Logarithmic and Quotient Function with Powers Expressed in terms of the Lerch Function. European Journal of Pure and Applied Mathematics, 14(4), 1337–1349. https://doi.org/10.29020/nybg.ejpam.v14i4.4085

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