Derivation of LC impedance transformation formula
I have not opened the links, but the general impedance transformation is described in any RF textbooks. I used Thomas Lee's and Razavi's books, because I am in IC domain.

Note: One generally uses LC oscillators because the Q factor of the resonator is very high. This results in a low phase noise for the same power. See Lesson's formula. On the other hand its bandwidth depends on the varactor tuning range and the varactors relative capacitance to the fixed capacitances. Usually the varactors Q is smaller then the other parasitic caps. In short, if one needs high tuning range, then usually not an LC oscillator is the solution. Ring oscillators or RC oscillators are better suited for this.