Those give you the derivation of the frequencies of the products. They are simply mixing products between the various fundamental tones applied along their harmonics. The harmonic series are essentially infinite, but their levels tend to decrease with higher order, so at some point you stop bothering with them. There is nothing fancy here, just two sets of harmonic series and all the sum and difference frequencies between every coice of two of them. Often the third order (2.Fa-Fb) and fifth order (3.Fa-2.Fb) are the interesting ones as lying close to the applied pair of fundamentals. You get the pait of intermod products in this area by the ambiguity in which you call a and which b.
As far as the levels go, they just use the relationship to the applied tones = the order number of the product without deriving it or referenceing somewhere with a derivation. This is much more involved to derive, and most people just wimp out and say "It just is" As a student, that looked dangerously like an assumption or something empirical, but the ratios came out to perfect integers at low levels and the mechanism was therefore an intriguing mystery. I once went through the derivation, but have never bothered since and don't have it in my head. It starts with assuming that levels are low enough that a simple power series makes a good model.
We've come an awful long way from FM tuners of any number of RF tuned circuits. Enough time and effort have gone by that you could have hand-filed one out of solid
Perhaps a significant fraction of time has gone by towards the powers that by closing down the FM broacast system in the UK. There have been rumblings in that direction, but they seem to have eased off recently in their efforts to shove DAB down our throats.
I don't think your goal is making a superb FM tuner any longer. There are plenty of quite decent models you can find at now-affordable prices and restore to full original condition. I bought one of the top-end Sony 'ES' models for twenty quid, and a Revox B261 (ex-BBC version) for £300. These killed off any feelings I had for making another home-brewed tuner. They were both good enough, and had some intriguing circuitry to keep the theoretician and designer in my head happy.
So I'm deducing that you've shifted into a curiosity mode regarding RF design techniques and some of the more intriguing limitations of current circuit techniques?
David