Power function and binomial series on T ( q , h )

This article is devoted to present -analogue of power function which satisfies additivity and derivative properties similar to the ordinary power function. In the light of nabla -power function, we present -analogue of binomial series and conclude that such power function is -analytic. We prove the...

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Bibliographic Details
Published in:Applied mathematics in science and engineering 2023-12, Vol.31 (1)
Main Authors: Gergün, Seçil, Silindir, Burcu, Yantir, Ahmet
Format: Article
Language:English
Subjects:
Taylor series
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Summary:This article is devoted to present -analogue of power function which satisfies additivity and derivative properties similar to the ordinary power function. In the light of nabla -power function, we present -analogue of binomial series and conclude that such power function is -analytic. We prove the analyticity by showing that both the power function and its absolutely convergent Taylor series solve the same IVP. Finally, we present the reductions of -binomial series to classical binomial series, Gauss' binomial and Newton's binomial formulas.
ISSN:2769-0911
2769-0911
DOI:10.1080/27690911.2023.2168657