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Finite and Infinite Generalized Back Ward q-Derivative Operator on its Application


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Authors : Vinoth Kumar C

Volume/Issue : Volume 8 - 2023, Issue 3 - March

Google Scholar : https://bit.ly/3TmGbDi

Scribd : https://bit.ly/439MmPL

DOI : https://doi.org/10.5281/zenodo.7809299

Abstract : In this paper, the author define the generalized q-derivative oprator and obtain its relation with shift operator.Also, we present the discrete version of Leibtz theorem according to the generalized qderivative operator.By defining its inverse,and using Stirling numbers of first kind, we establish formula for the sum of higher power of geometric progression in the field of first of Number Analysis.

Keywords : Generalized q-Derivative Operator, Polynomial Factorial, Geometric Progression

In this paper, the author define the generalized q-derivative oprator and obtain its relation with shift operator.Also, we present the discrete version of Leibtz theorem according to the generalized qderivative operator.By defining its inverse,and using Stirling numbers of first kind, we establish formula for the sum of higher power of geometric progression in the field of first of Number Analysis.

Keywords : Generalized q-Derivative Operator, Polynomial Factorial, Geometric Progression

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