Tagged Questions

2
votes
2answers
192 views

Chain rule for discrete/finite calculus

In the context of discrete calculus, or calculus of finite differences, is there a theorem like the chain rule that can express the finite forward difference of a composition $∆(f\circ g)$ in ...
0
votes
1answer
77 views

Sum $\sum_{k=0}^n p(k) \cdot f(k)$ in terms of $f(n)$ and $\sum_{k=0}^n f(k)$

I am aware of that this question shall be rather basic, and that there may be a lot of resources on this, but it is quite complicated to use Google to find relevant results for this (I have not found ...
1
vote
2answers
847 views

Function as parameter in Wolfram Mathematica

I want to define some basic functions known from "discrete analysis": $$I(f)(x):=f(x)$$ $$E(f)(x):=f(x+1)$$ $$\Delta(f)(x) := (E-I)(f)(x) = f(x+1)-f(x)$$ $$\nabla(f)(x) := (I-E^{-1})(f)(x) = ...
2
votes
0answers
129 views

Discrete-analytic functions [closed]

I do not know if such concept already exists but lets consider functions which are equal to its Newton series. We know that functions which are equal to their Taylor series are called analytic, so ...