@reiver

What is Quantum Calculus

Consider the following expression:

f ( x ) - f ( x 0 ) x - x 0

As x approaches x 0 , the limit, if it exists, gives the familiar definition of the derivative d f d x of a function f ( x ) at x = x 0 . However, if we take x = q x 0 . or x = x 0 + h . where q is a fixed number different than 1 , and h a fixed number different from 0 , and do not take the limit, we enter the fascinating world of quantum calculus: The corresponding expressions are the definitions of q-derivative and h-derivative of f ( x ) . Beginning with these two definitions [...] two types of quantum calculus, the q-calculus and h-calculus [are developed].

-- Victor G. Kac , Pokman Cheung

from "Quantum Calculus"

Quoted on Tue Nov 20th, 2012