All analitic function can be express how: [tex]f(x) = \frac{1}{0!} \frac{d^0f}{dx^0}(x_0) (x - x_0)^0 + \frac{1}{1!} \frac{d^1 f}{dx^1}(x_0) (x - x_0)^1 + \frac{1}{2!} \frac{d^2f}{dx^2}(x_0) (x - x_0)^2 + \frac{1}{3!} \frac{d^3f}{dx^3}(x_0) (x - x_0)^3 + ...[/tex] that is the taylor series of the function f(x).(adsbygoogle = window.adsbygoogle || []).push({});

Analogously, should exist a taylor series that use the discrete derivative ##\frac{\Delta f}{\Delta x} = f[x+1] - f[x]##. I found this in wolframpage http://mathworld.wolfram.com/ForwardDifference.html but appears strange. I didn't undertood what such series means. Someone can explain me?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Taylor series in terms of discrete derivative

**Physics Forums | Science Articles, Homework Help, Discussion**