A Note on q-Derivative Operator and Divided Difference

Abstract:

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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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$35.00

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