Coefficients for finite difference approximation in Python (meth. of undetermined coefficients)

Dear Daniel. I believe my question is pretty straightforward: I have a function in Matabl, I want a similar one in Python.
 
It's 'divided differences'. Finite difference is different and talking about coefficients is nonsense in that case.

Have you checked numpy, scipy
https://docs.scipy.org/doc/numpy/reference/generated/numpy.diff.html


These techniques are highly unstable and ill-posed in general. Better not to use it. And I have never used it myself.

Out of curiosity, what's the problem to be solved?
 
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Thank you Daniel..
Educational purpose only.. I am in quarantine from work so I have deicded to spend time learning numerical analysis. I managed to buy a copy of
Randy LeVeque -- Finite Difference Methods for ODEs and PDEs (the only book available at the university bookshop close to my home in Denmark, Copenhagen.)

I am simply trying to play around the concepts introduced in chapter 1 but I don't have Matlab license (too expensive).
 
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