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.

• Periodical: Applied Mechanics and Materials (Volumes 50-51)
• Pages: 377-381
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.50-51.377
• Online since: February 2011
• Authors: Feng Cui
• Keywords: Divided Difference, q-Derivative, q-Leibnitz Formula

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