In order to make a curve passing via points, I use a parabola basic interpolation function and would like to use a correction function for passing precisely through the points.
The correction function should pass via the coordinates given in the link below (see screen copy of it).
In my opinion, the best curve passing through these points is a gamma function (vertical tangent at 0/-1/-2/-3..; an extreme in between, in the case of the graph below horizontal at 1).
(I have tried log exp polynom etc. all ok and not good enough).
In order to find the best gamma (= a gamma of interval [-5.667,-5]?), I would like to see the derivate of the gamma function and will compare it with a manually done derivate curve of the points in the attachments/link.
(I have tried a gamma interpolation based on the gamma curve between [0,1.46] but this is not good enough).
Now, how looks the first derivative of the gamma function? I found some place with the gamma (here https://www.desmos.com/calculator/b2cbb6bfig?lang=th ), but not for the gamma derivative. Wikipedia gives some hints but this is limited. Any visual representation of gamma derivative is welcome (books, internet link, pc programs, interactive drawing like desmos..).
So, any advice is welcome for my small project:
visual identification of correction curve based on gamma (in this thread: quicker identification via visual inspections of gamma derivatives)
calculation of a gamma interpolation curve (I have all numerical power to do it on my PC)
