I have having difficulty in how to solve the following double integral problem involving absolute values and the assumption that $\alpha > 1$:
$\iint_{-\infty}^{+\infty} \frac{1}{1+|x|^\alpha} \frac{1}{1+|y|^\alpha} \frac{1}{1+|x-y|^\alpha} \,dx\,dy$
Any tips on how to calculate the above integration is highly appreciated. Thank you in advance!
The double integral can be split into several integrals involving only trigonometric functions. But these integrals cannot be expressed in terms of a finite number of standard functions. So, it is doubtful that a closed form could be obtained to express the double integral :