Power function and binomial series on (q,h)

This article is devoted to present $ (q,h) $ -analogue of power function which satisfies additivity and derivative properties similar to the ordinary power function. In the light of nabla $ (q,h) $ -power function, we present $ (q,h) $ -analogue of binomial series and conclude that such power functi...

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Bibliographic Details
Published in:Applied mathematics in science and engineering 2023-12, Vol.31 (1)
Main Authors: Seçil Gergün, Burcu Silindir, Ahmet Yantir
Format: Article
Language:English
Subjects:
(q, h) $ -analytic functions
gauss' binomial formula
nabla $ (q, h) $ -binomial series
nabla $ (q, h) $ -power function
nabla generalized quantum binomial
newton's binomial formula
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Summary:This article is devoted to present $ (q,h) $ -analogue of power function which satisfies additivity and derivative properties similar to the ordinary power function. In the light of nabla $ (q,h) $ -power function, we present $ (q,h) $ -analogue of binomial series and conclude that such power function is $ (q,h) $ -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 $ (q,h) $ -binomial series to classical binomial series, Gauss' binomial and Newton's binomial formulas.
ISSN:2769-0911
DOI:10.1080/27690911.2023.2168657