In the context of mathematical physics, a collaborator and I stumbled upon a physical quantity expressed in terms of the following rational function:
$$ f(x_1, \dots, x_m;y_1,\dots, y_n) = \frac{\prod_{a,b=1}^m (1+x_ax_b) \prod_{a,b=1}^n (1+y_ay_b)}{\prod_{a=1}^m \prod_{b=1}^n (1+x_ay_b)^2} .$$
It appears to have a nice structure (in particular, it is symmetric in either set of '$x$' and '$y$' variables). Has this function been studied before and/or does it appear elsewhere in the mathematical literature?