Double Integral of Logarithmic and Quotient Rational Functions Expressed in Terms of the Lerch Function
Abstract
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 and express it in terms of the Lerch function. 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. The majority of the results in this work are new.
 Publication:

Symmetry
 Pub Date:
 September 2021
 DOI:
 10.3390/sym13091708
 arXiv:
 arXiv:2106.03551
 Bibcode:
 2021Symm...13.1708R
 Keywords:

 Mathematics  General Mathematics;
 3002;
 30D10;
 30D30;
 30E20;
 11M35;
 11M06;
 01A55