I have the following:
$\lambda_1 = \frac{const_{A}}{value1_1} + \frac{const_{B}}{value2_1} + \frac{const_{c}}{value3_1} $
$\lambda_2 = \frac{const_{A}}{value1_2} + \frac{const_{B}}{value2_2} + \frac{const_{c}}{value3_2} $
$ ... $
$\lambda_n = \frac{const_{A}}{value1_n} + \frac{const_{B}}{value2_n} + \frac{const_{c}}{value3_n} $
Where $n \approx 400$, and $(value_{1_n}, value_{2_n}, value_{3_n})$ alongside all $\lambda_n$ are known values.
Aim
I aim to create a function from this set of data that correctly describes $\lambda(n)$ for all n.
ie I think the solution's final form may take...
$\lambda_n = \left( \lambda_n = \frac{const_{A}}{value1_n} + \frac{const_{B}}{value2_n} + \frac{const_{c}}{value3_n} \right) * [SomeComplicatedCalibrator]$
Please could someone help? A full solution would be literally amazing, but ideas welcome :)
If someone could reply with suitable tags, I'll update the post too. I literally don't know what to even put haha.
I don’t think it’s possible through the way you’re trying. If you know the results, and you know the denominators; then you can multiply every result by every denominator, which will sort of simplify searching for what the constants A B and C may be. If there were only two constants, X and Y, then that would be a function Z(n) = blahX + blahblahY. With 400 equations to satisify, it seems too easy to have at least two contradicting Z(n), such that no single values to X and Y can satisfy all 400 of the equations. And that’s for just two variables; you ask for three.
Instead, I suppose, I recommend you learn about generating functions. They take some selected set of numbers, such as your lambda(n), and assign them as the coefficients to a Taylor series, and then attempt to confusingly reverse-engineer it to find whatever function has that Taylor series, since every Taylor series is unique.
This isn’t exactly an answer, but I don’t have enough renown to comment. My apologies.