I think you've misunderstood what he wants to achieve.
He wants his pitch wheel to go one octave down when he moves it from the center-position to the lowest position, and only two semitones up when he moves it from center-position to the highest position. In other words, he does not want even changes between the highest and lowest positions of the pitch wheel.
However, I still agree that there is no need for advanced maths here. Simple fractions and conditionals will do.
There are two ways to do this. One is to fill the exact pitch-range of 14 semitones (12 down, 2 up) or to use part of a 24 semitone span (12 down, 12 up). For the sake of learning as much as possible, I'm going to do it the most difficult way first. For those who just want a simple answer to what to do, skip to the end of the second way, and you'll find a formula to paste into FL.
First off, since a span of -12 to +2 is desired, one needs a total range of 14 semitones. Since FL specifies these using only one variable which describes semitones up/down, you would have to instruct FL to pitch-bend from -7 to +7. This can be done by changing the number next to the pitch-knob to 7.
At that point, you will have gained if nothing else, the desired range. The rest can be done with the formula-editor of FL. Simply right-click the pitch-knob and select "Link to controller..." to get to the Remote control settings.
What you know is that you want it to distribute the twelve first semitones over the first 0.5 values of input, and the final two over the input span from 0.5 to 1. The formula editor provides you with pretty much everything you need, without the need for estimates using taylor/fourier series.
For the first half of the input, you want it to go from 0 to 12/14. This can be done using the IfL(a,-function, which equals 1 when a is less than b. As such, to leave the pitch-bend null and void from 0.5 and up, all you'd have to do is change the formula from Input to IfL(Input,0.5)*Input. Now you'll have a graph that goes halfway up, and then drops to zero again. Then you translate these values to the desired pitch-range, and end up with the following formula for pitch-bending one octave down:
Now all you have to do is do the same for the two semitones up, using IfGE(a,, which equals 1 when a is greater than or equal to b. (Using this instead of IfG(a, ensures that it doesn't go one octave down when the pitch-wheel is centered). You then distribute those values over the two semitones up, and you add the two together.
(IfL(Input,0.5)*input*24/14) + (IfGE(Input,0.5)*((Input-0.5)*2/14)+(IfGE(Input,0.5)*12/14))
Now, since FL wasn't designed to pitch-bend with non-equal range up and down, you're left with an offset in pitch.
When we line up the various pitch-alterations, we get the following two sets of semitones.
FL -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 You -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 *
So when we want the pitch-bend to remain neutral (no change in pitch), it's actually going five semitones up. Of course, by right-clicking the note 5 semitones up on the piano-roll (ie: the F above your C), you correct this offset, and you now have the desired range behaving the way you were hoping.
The second way removes the need for the offset in notes by creating the entire span of 12 notes in each direction, and then only using part of it.
First, set the number of semitones you want to bend with to 12 in the box next to the pitch-knob. Since the first half is already correct, you can start out by setting the formula to IfL(Input,0.5)*Input. Now you just need to make sure it doesn't go beyond two semitones up. This can be done by simple math, since you know that you want it to occupy an area of 2 semitones, starting halfway up. At this point, you're all probably very tired of thinking and just want the results, so I'm just going to copypaste the formula here:
(IfL(Input,0.5)*Input) + ((IfGE(Input,0.5)*2*Input/12)+(IfGE(Input,0.5)*10/24))
Now, at the end here, a small and boring description of why this method is better than using taylor/fourier series. Taylor/Fourier-series work by using sine or cosine to create an approximation of a function. This is the foundation for the fourier transform, which is used rather frequently in many of the VSTs we all know and love. However, to get a close approximation of even just a simple linear function, like the standard pitch-bend from -2 to +2, you need an awful lot of sinewave-components, and you're still going to get errors, and when you're going to use it with a pitch-wheel... well, you want to do the pitch-bend thing, you don't want it to sound like an LFO ate your pitch. Taylor/Fourier series are also subject to a lot of errors near edges, like the end-points of a saw-wave (discontinuous functions), and that is likely to appear also with the approximation in this case.