Paper Title:
A Note on q-Derivative Operator and Divided Difference
  Abstract

The q-analogue of the derivative operator is playing a more and more important role in mathematics and physics. Moreover, the divided difference, as an important and classical mathematical tool with a close relation to the derivative, is also used in many fields. In this paper, the connection between the q-derivative and the divided difference is investigated such that the q-derivative can be understood better. The q-derivative of higher order of a function f can be represented by the divided difference of f at some special nodes. Furthermore, the result is used to provide a new and easier proof of q-Leibnitz formula and its generalization.

  Info
Periodical
Edited by
Shaobo Zhong, Yimin Cheng and Xilong Qu
Pages
377-381
DOI
10.4028/www.scientific.net/AMM.50-51.377
Citation
F. Cui, "A Note on q-Derivative Operator and Divided Difference", Applied Mechanics and Materials, Vols. 50-51, pp. 377-381, 2011
Online since
February 2011
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