Power function and binomial series on T-(q,T-h)
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING, cilt.31, sa.1, 2023 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 31 Sayı: 1
- Basım Tarihi: 2023
- Doi Numarası: 10.1080/27690911.2023.2168657
- Dergi Adı: APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: Nabla generalized quantum binomial, nabla (q, h)-power function, (q, h)-analytic functions, nabla (q, h)-binomial series, Newton's binomial formula, Gauss' binomial formula
- Dokuz Eylül Üniversitesi Adresli: Evet
Özet
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.