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

Gergün S., Silindir Yantır B., Yantir A.

APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING, cilt.31, sa.1, 2023 (SCI-Expanded) identifier identifier

  • 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.