A Note on the q-Derivative Operator

Abstract

The following statement is proved. If the q-derivative operator Dq is defined by [formula] for functions f(hook) which are differentiable at x = 0, then we have for every positive integer n[formula] for every function f(hook) whose nth derivative at x = 0 exists. We give a proof in both the real variable and the complex variable case. © 1993 Academic Press, Inc.