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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-12-01
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| Series: | Applied Mathematics in Science and Engineering |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/27690911.2023.2168657 |
| 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. |
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| ISSN: | 2769-0911 |