What is Quantum Calculus
Consider the following expression:
As approaches , the limit, if it exists, gives the familiar definition of the derivative of a function at . However, if we take . or . where is a fixed number different than , and a fixed number different from , 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 . Beginning with these two definitions [...] two types of quantum calculus, the q-calculus and h-calculus [are developed].
from "Quantum Calculus"
Quoted on Tue Nov 20th, 2012