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And here is the plot of indefinite sum of tan(x): Here you can see tan(x) in red and its indefinite sum is in blue. As you can see, the indefinite sum is fairly continuous. Oleg Eroshkin's conclus …

Well I found the answer to your question, it is $$\sum_x \tan(x)=ix-\psi _{e^{2 i}}^{(0)}\left(x+\frac{\pi }{2}\right)+C$$ I have verified it with difference operator and it gives tan(x). The functi …

From this answer of mine The antidifference of tangent is: $$\sum_z\tan z=\sum _{k=1}^{\infty } \left(\psi \left(k \pi -\frac{\pi }{2}+1\right)+\psi \left(k \pi -\frac{\pi }{2}\right)-\psi \left(k \p …

No, this is not true. For instance, for function $(10(1-e^{-1/x^2})-9)+\exp(x)$ and $f(0)=2$ all the consecutive derivatives are positive at $x=0$, while the first difference is not. For function $f …

if a Newton series exists that p is actually a constant function. Not exactly so. The solutions are always a set of functions different by a constant term. But among these solutions the one which is …