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

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

APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING, vol.31, no.1, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 31 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1080/27690911.2023.2168657
  • Journal Name: APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: 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 University Affiliated: Yes

Abstract

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.