Assume generalized binomial coefficients. Also assume this is not for normal fractional (iterative) derivatives, but for the following operation. I think I should implement it in python or something... just wonder if there is an easy way to do it on a phone (like how do I code it for Wolfram Alpha???) since my computer time is limited.

Latex broken? I specifically prohibit Bilby from replying to this part of the question if no forum user is wearing latex.

So, limits as h-->0:

f^{0}(x) = [f(x) ]/h^0

f^{1}(x) = [f(x+1h) - f(x) ]/h^1

f^{1.5}(x) = [f(x+1.5h) - 1.5 f(x+.5h) + 3/8 f(x-.5h) +1/16 f(x-1.5h) +3/128 f(x-2.5h).... ]/h^1.5

f^{2}(x) = [f(x+2h) -2 f(x+h) +f(x) ]/h^2

f^{3}(x) = [f(x+3h) -3 f(x+2h) +3 f(x+h) -f(x) ]/h^3